gmat problem solving strategies

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How to Master GMAT Problem Solving

Stacey Koprince - Manhattan Prep

Stacey Koprince is an mba.com Featured Contributor and the content and curriculum lead and an instructor for premier test prep provider Manhattan Prep .

The GMAT™ exam feels like a math test, especially GMAT Problem Solving problems. They read just like textbook math problems we were given in school; the only obvious difference is that the GMAT Quant section gives us five possible answer choices.

It’s true that you have to know certain math rules and formulas and concepts, but actually, the GMAT is really not a math test. First of all, the test doesn’t care whether you can calculate the answer exactly (e.g., 42). It cares only that you pick the right answer letter (e.g., B)—and that’s not at all the same thing as saying that you have to calculate the answer exactly, as you did in school.

More than that, the GMAT test-writers are looking for you to display quantitative and critical reasoning skills (the section is literally called Quantitative Reasoning ); in other words, they really want to see whether you can think logically about quant topics. They’re not interested in testing whether you can do heavy-duty math on paper without a calculator. And here’s the best part: They build the problems accordingly and you can use that fact to make GMAT Problem Solving problems a whole lot more straightforward to solve. I’ll show you how in this article!

GMAC’s team (aka, the people who make the GMAT) gave me three random problems to work through with you. I had no say in the problems; I didn’t get to choose what I liked. Nope, these three are it, and every single one illustrates this principle: The GMAT is really a test of your quantitative reasoning skills, not your ability to be a textbook math whiz.

GMAT Quant is not a math test

Okay, let’s prove that claim I just made. Grab your phone and set the timer for 6 minutes. (If you’ve been granted 1.5x time on the GMAT, set it for 9 minutes. If you’ve been granted 2x time on the GMAT, set it for 12 minutes.)

Do the below 3 problems under real GMAT conditions:

• Do them in order. Don’t go back.
• Pick an answer before you move to the next one. (Don’t just say you’re not sure and move on. Make the guess, as you have to do on the real test.)
• Have an answer for all the problems by the time your timer dings—even if your answers are random guesses.

Problem #1: Fellows in the org

According to the table above, the number of fellows was approximately what percent of the total membership of Organization X? 

(A) 9% (B) 12% (C) 18% (D) 25% (E) 35%

Problem #2: Yolanda and Bob

One hour after Yolanda started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolanda’s walking rate was 3 miles per hour and Bob’s was 4 miles per hour, how many miles had Bob walked when they met?

(A) 24 (B) 23 (C) 22 (D) 21 (E) 19.5

Problem #3: Oil cans

Two oil cans, X and Y, are right circular cylinders, and the height and the radius of Y are each twice those of X. If the oil in can X, which is filled to capacity, sells for $2, then at the same rate, how much does the oil in can Y sell for if Y is filled to only half its capacity? 

(A) $1 (B) $2 (C) $3 (D) $4 (E) $8

Time’s up! Do you have an answer for each problem? If not, make a random guess—but do choose an answer for every problem.

You probably want me to tell you the three correct answers so you’ll know whether you got them right. But I’m not going to.

We’re going to review these in the same way that I want you to review them when you’re studying on your own—and that means *not* looking up the correct answer right away. 

• How confident are you about this problem?
• Did/do you have another idea for how to solve? Try it now.
• Were you straining to remember some rule or formula? Look it up and try again.
• Still stuck? Okay, look at the correct answer. Does knowing that give you any ideas? Push them as far as you can. 
• Stuck again? Start to read the explanation. Stop as soon as the explanation gives you a new idea. Push it as far as you can before you come back to the explanation again.

Basically, push your own thinking and learning as far as you can on your own. Use the correct answer and explanation only as a series of hints to help unstick yourself when you get stuck.

Okay, let’s dive in!

GMAT Problem Solving #1: Estimate

We’re going to use the UPS solving process: Understand, Plan, Solve. (A mathematician named George Polya  came up with this.) Use this rubric to approach any quant-based problem you ever have to figure out in your life!

The basic idea is this: Don’t just jump to solve. (That’s panic-solving! We’ve all been there. It does not end well.) Understand the info first. Come up with a plan based on what you see. Only then, solve. 

And if you don’t understand or can’t come up with a good plan? On the GMAT, bail! Pick your favorite letter and move on. UPS can help you know what to do and what not to do.

Glance at the answers. Yes, before you even read the problem! 

The answers indicate that this is a percent problem and they’re also pretty decently spread apart. One is a little less than 10% and another is a little greater than 10%, so that’s one nice split. The remaining three are a little less than 20%, exactly 25%, and about 33%, otherwise known as one-third. Those are all “benchmark,” or common, percentages, so now I know I can probably estimate to get to my answer. Excellent.

And then the problem actually includes the word approximately ! Definitely going to estimate on this one.

Start building a habit of glancing at the answers on every single Problem Solving problem during the Understand phase, before you even think about starting to solve. (And yes, I really do glance at the answers before I even read the question stem!)

Here are some examples of the types of answer-choice characteristics that indicate there’s a good chance you’ll be able to estimate at least a little:

• The answers are really spread out (e.g., 10, 100, 300, 600, 900)
• Some are positive and some are negative
• Some are less than 1 and some are greater than 1
• They’re spread out on a percent scale (0 to 100) or on a probability scale (0 to 1)—less than half, greater than half, etc.

Next, there’s a table with a bunch of categories and each category is associated with a specific number. What does the question ask?

It wants to know the Fellows as a percent of the total. That’s a fraction with fellows on the top and the total of all members on the bottom:

The Fellows category is already listed in the table. Great, that’s the numerator.

What about the total? That means adding up all the numbers in the table without a calculator or Excel. Rolling my eyes. And that’s how I know that I will not be doing “textbook math” here. Pay attention to those feelings of annoyance! There’s some other easier, faster path to take. Use your Plan phase to find it.

I need the Total. I can estimate. Look at the collection of numbers. Can you group any into pairs that will add up to “nicer” numbers—numbers that end in zeros?

Here’s one way: 

• Honorary is a tiny number compared to the rest. Ignore it. 
• Fellows are a little under 10,000 and Members are a bit over 35,000. Group them. 
• Associates are a little less than 28,000 or a little more than 2,000 away from 30,000. And Affiliates are a little over 2,000! Combine those two groups.

We’re already spilling into the solve stage on this one. Fellows and Members together are about 45,000. Associates and Affiliates together are about 30,000. Altogether, there are 75,000 members:

That goes on the bottom of the fraction. Fellows go on top. They’re about 9,200, so let’s call that 9,000. Make a note on your scratch paper that you’re underestimating —just in case you need to use that to choose your final answer. I use a down-arrow to remind myself.

How to simplify 9 out of 75? Both of those numbers are divisible by 3.

Ok, 3 out of 25: what percent is that? We normally see percentages as “out of 100.” Hmm. 

If you multiply the denominator by 4, that gets you to “out of 100.” And whatever you do to the denominator, you have to do to the numerator, so the fraction turns into 12 out of 100, or 12%.

12% is in the answers; the next closest greater value (since we slightly underestimated) is 18%. That’s too far away, so the only answer that makes sense is (B).

Notice how the numbers looked really ugly to start out, but as soon as you started estimating, they combined and simplified really nicely? It’s not just luck. The test-writers know you don’t have access to a calculator, so they’re building the problems to work out nicely if you use these types of approaches. They actually want to reward you for using the kind of quantitative reasoning that you’d want to use at work and in business school.

You can certainly solve GMAT Problem Solving problems using traditional textbook math approaches. You’ll just do a lot more work that way. And using textbook approaches won’t actually help train your brain for the kind of analytical thinking about quant that you’ll need to do in business school or in the working world.

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GMAT Problem Solving #2: Logic (and draw!) it out

One hour after Yolanda started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolanda’s walking rate was 3 miles per hour and Bob’s was 4 miles per hour, how many miles had Bob walked when they met? 

The answers are real values and on the smaller side. They’re pretty clustered, so probably won’t be estimating on this one. Four of the five are integers. I wonder whether I can work backwards on this one (i.e., just try some of the answers)?

This problem is what I call a Wall of Text—a story problem. Get ready to sketch this out. Take your time understanding the setup; if you don’t “get” the story, you’ll never find the right answer. (And if you don’t get the story, that’s your clue to guess and move on.)

There are two people, 45 miles apart, and they’re walking towards each other. Normally, I’d only write initials for the two people, but annoyingly, Yolanda shares her initial with one of the locations.

The first sentence has a critical piece of info that’s easy to gloss over: Yolanda starts first, an hour before Bob. 

It’s super annoying that they don’t start at the same time. I don’t know what to do about that yet, but I’m noting it because I want to think about that when I get to my Plan stage. Again, pay attention to whatever annoys you about the problem! That’s why I put START FIRST in all-caps on my scratch paper.

Next, Yolanda walks a little slower than Bob. Add that to your diagram.

Finally, the problem asks who walked further by the time they meet—and how far that person walked. If Yolanda and Bob had started at the same time, then I’d know Bob walked farther, since he’s walking faster, but Yolanda started first, so I can’t tell at a glance. Still annoyed by that detail.

The two people have to cover 45 miles collectively in order to meet somewhere in the middle. Glance at the answers again. There are two sets of pairs that add to 45: (A) 24 and (D) 21 and (B) 23) and (C) 22. 

On a problem like this one, the most common trap answer is going to be solving for the wrong person (in this case, Yolanda instead of Bob). So the correct answer is going to fall into one of those pairs, because then the most common trap answer will also be built into the problem. The other pair will represent some common error when solving for Bob—and then also mistakenly solving for Yolanda instead. But answer (E) 19.5 doesn’t have a pairing, so it has no built-in trap. If you have to guess, don’t guess the unpaired answer, (E).

Once I subtract the 3 miles that Yolanda walked alone, the two of them together have 42 more miles to cover before they meet. I did note the extra 3 miles she walked off to the side just in case.

Bingo. Now I know how I’m going to solve this problem, because now it’s a more straightforward rate problem.

From here, you can do the classic “write some equations and solve” approach to rates problems. But I’m going to challenge you to keep going with this Logic It Out approach we’re already using—both because it really is easier and because it’s what you would use in the real world. You’re not getting ready to take the GMAT because you want to become a math professor. You’re doing this to be able to think about quant topics in a business context. So make your GMAT studies do double-duty and get you ready for b-school (and work!) as well.

Back to Bob and Yolanda. They’re 42 miles apart and walking towards each other. Every hour, Yolanda’s going to cover 3 miles and Bob’s going to cover 4 miles, so they’re going to get 7 miles closer together. Together, they’re walking 7 miles per hour.

When two people (or cars or trains) are moving directly towards each other, you can add their rates and that will tell you the combined rate at which they’re getting closer together. (You can do the same thing if the two people are moving directly away from each other—in this case, the combined rate is how fast they’re getting farther apart.)

One more thing to note: The distance still to cover is great enough (42 miles) compared to their combined rate (just 7 mph) that Bob is going to “overcome” the 3 miles that Yolanda walked on her own first. So Bob covered a greater distance than Yolanda did. The answer is going to be one of the two greater numbers in the pairs: (A) 24 or (B) 23.

So Yolanda and Bob are getting closer together at a rate of 7 miles each hour and they have a total of 42 miles to cover until they meet. How long is it going to take them?

Divide 42 by 7. They’re going to meet each other after 6 hours on the trail. At this point, Bob has spent a total of 6 hours walking, but not Yolanda! She started first, so she spent a total of 6 + 1 = 7 hours walking. The question asks how far Bob walked: 4 miles per hour for 6 hours, or a total of (4)(6) = 24 miles. 

The correct answer is (A).

If you’d solved for Yolanda first, you’d have gotten (3 miles per hour)(7 hours) = 21 miles. That’s in the answer choices, but it’s less than half of the total distance, so she wasn’t the one who walked farther. In other words, answer (D) is a trap.

Even if you do know how to solve the problem, it’s important to have done that earlier thinking to realize that the answer must be (A) or (B). That way, when you solve for Yolanda, you won’t accidentally fall for answer (D), since Yolanda’s distance is in the answer choices.

When the problem talks about two people or two angles in a triangle or two whatevers and the problem also tells you what they add up to, the non-asked-for person/angle is almost always going to show up in the answer choices as a trap. You do the math correctly, but you accidentally solve for x when they asked you for y . We’ve all made that mistake. 

Noticing that detail earlier in your process is a great way to avoid accidentally falling for the trap answer during your Solve phase.

(Have Polya and I sold you yet on using the UPS process? I hope so.)

Should I Retake the GMAT?

Should you retake the GMAT, and does retaking the GMAT look bad? Manhattan Prep’s Stacey Koprince answers the most common retake the GMAT questions.

GMAT Problem Solving #3: Draw it out; Do arithmetic, not algebra; Choose smart numbers

Glance at the answers. Small integers. Kind of close together, so estimation might not be in the cards, but perhaps working backwards (try the answer choices) could work, depending on how the problem itself is set up. (I don’t know yet because I haven’t actually read the problem.)

Now I’m part-way into the first sentence and see the word cylinders . Overall, I’m not a fan of geometry and I really dislike 3D geometry in particular. So as soon as I see that word, part of my brain is thinking, “If this is a hard one, I’m out.”

But I’m going to finish reading it before I decide. Let’s see. Two cylinders, and then they give me some relative info about the height and radius. They’re probably going to ask me something about volume, since the volume formula uses those measures, and scanning ahead: yep, volume.

So now I know I need to jot down the volume formula and I’m also going to draw two cylinders and label them.

I’m going to make sure I note really clearly what I’m trying to solve for. On geometry problems in particular, it’s really easy to solve for something other than the thing they asked you for. And on this one, I’m also making an extra note that the larger cylinder is only half full. I both wrote that down and drew little water lines in the cylinders to cement that fact in my brain.

This is a complex problem, so just pause for a second here. Do you understand everything they told you, including what they asked you to find? If not, this is an excellent time to pick your favorite letter and move on.

If you are going to continue, don’t jump straight to solving. Plan first. (And if you can’t come up with a good plan, that’s another reason to get out.)

The thing that’s annoying me: They keep talking about the dimensions for the two cylinders but they never provide real numbers for any of those dimensions. And boom, now I know how I’m going to solve. When they talk about something but never give you any real numbers for that thing, you’re allowed to pick your own values. Then you can do arithmetic vs. algebra—and we’re all better at working with real numbers than with variables.

My colleagues  and I call this Choosing Smart Numbers. The “Smart” part comes from thinking about what kinds of numbers would work nicely in the problem—make the math a lot less annoying to do.

We usually avoid choosing the numbers 0 or 1 when choosing smart numbers because those numbers can do funny things (e.g., multiplying with a 0 in the mix will always return 0, regardless of the other numbers involved).

And if we have to choose for more than one value, we choose different values. Finally, as I mentioned earlier, we’re looking to choose values that will work nicely in the problem. (Most of the time, this means choosing smallish values.)

Finally, before I start solving, I’m going to ask myself two things: What am I solving for and how much work do I really need to do?

I’m trying to figure out how much oil is in the larger (but only half-full!) cylinder. I know that the full capacity of the smaller cylinder costs $2 and that the oil is charged at the same rate for the larger one. So if I can figure out the relative amount of oil in the larger cylinder, I can figure out how much more (or less) it will cost. For example, if it turns out that the larger cylinder contains twice as much oil as the smaller one, then the cost will also be twice as much.

In the volume formula, the radius has to be squared while the height is only multiplied, so I want to make the radius a lower value. I’m going to choose r = 2 and h = 3.

Use those values to find the relative volumes of the two cylinders. Reminder yet again: The larger cylinder is only half full, so multiply that volume by one-half:

What’s the relative difference between the two? They both contain pi, so ignore that value. The difference is 12 to 48—if you multiply 12 by 4, you get 48.

So the money will also get multiplied by 4: Since the oil in the smaller cylinder costs $2, the oil in the larger one costs (2)(4) = $8. The correct answer is (E).

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Understand, plan, solve on GMAT Quant

Whenever you solve any GMAT Problem Solving (PS) or Data Sufficiency (DS) problem, follow the Understand, Plan, Solve process. Print out this summary and keep it by you when you’re studying:

• Glance at the answers (on PS) or the statements (on DS) and the question stem. Anything jump out—an ugly equation, a diagram, an indication that you might be able to estimate, etc?
• Read the question stem. Focus just on understanding what it’s telling you and what it’s asking you.
• Jot down what it’s asking, along with any other useful info (equations, etc.). Don’t solve! Just jot (write or sketch).
• Reflect on what you know so far. Lost? Guess and move on. But if you do understand everything, then consider what your best plan is. Can you estimate anywhere? How heavily? Can you use a real number and just do arithmetic? Is there a way to draw or logic it out? What are they really asking you? This reflection is how I realized I just needed a relative value on the Oil Cylinders problem.
• Organize your thoughts and your scratch work to get set up for the Solve stage. Maybe you need to redraw or add something to your diagram, as I did for Yolanda and Bob. Maybe you need to group the data or equations a little differently, as I did on the Membership problem.
• Don’t have a plan you feel pretty good* about? Forget it—guess and move on. (*You don’t have to feel 100% confident. But you want to feel like it’s a decent plan. If you don’t, let it go.)
• Be systematic. You’re almost there. Write your work down. Don’t try to compress steps or work more quickly than is comfortable for you. Keep your scratch paper organized.
• Don’t do more work than you have to. Estimate when you can. Keep an eye on the answers as you work. Eliminate impossible answers as you go. Stop as soon as only one answer letter is left.
• Be willing to bail. Even if you understand and have a decent plan, you still might get stuck. Don’t start trying some other plan at that point. Something’s not working with this one; guess and go spend your time on a better opportunity later in the test.

Finally, remember your overall goal here: You want to go to business school. The point is not to show how much of a mathematics scholar you are. The point is to learn how to think logically about quant topics—with, yes, some amount of actual textbook math tossed in there. 

Actively look for the Logic It Out / Draw It Out / Quick and Dirty approaches. They’ll not only save you time and stress on GMAT Problem Solving and Data Sufficiency, but they’ll also help train your brain for quant discussions in business school and in the boardroom.

Want more strategies to improve your GMAT Problem Solving skills? Sign up for Manhattan Prep’s free GMAT Starter Kit  and check out the section on Foundations of Math.

Happy studying!

She’s been teaching people to take standardized tests for more than 20 years and the GMAT is her favorite (shh, don’t tell the other tests). Her favorite teaching moment is when she sees her students’ eyes light up because they suddenly thoroughly get how to approach a particular problem.

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4 Tips to Tackle GMAT Math Problem Solving Questions

GMAT Problem Solving questions make up roughly half of the 31 questions in the GMAT's Quantitative section. That means you’ll typically see 15 or 16 Problem Solving questions. Perfecting your approach and pacing on these questions can go a long way toward improving your score on the GMAT .

GMAT Problem Solving the GMAC Way

In Problem Solving questions, you need to solve a math problem and pick the correct answer from among five answer choices. Let’s review what GMAC says about Problem Solving questions.

The Quantitative section tests three broad content areas:

All of the rules and concepts from these areas that are tested are generally covered in high school mathematics classes. The Problem Solving format is designed to test basic mathematical skill and understanding of elementary concepts from the three content areas. Moreover, Problem Solving also tests the ability to reason quantitatively, solve quantitative problems, and interpret data presented in the form of graphs. In other words, some GMAT Problem Solving questions are really just testing your ability to follow the rules. Other GMAT Problem Solving questions, the ones that test your ability to reason quantitatively, are testing your ability to determine which rules apply before you start solving. 

Read More: GMAT Practice Questions

Tips for GMAT Math Problems

1. remember what the gmat tests..

Some GMAT questions entice you to use math that is actually more sophisticated than you really need for the GMAT. It’s not that you can’t solve the questions using sophisticated math. It’s just that doing so may take more time than you really have. However, there’s often a simpler—and faster—approach that involves little more than some basic math. Keeping that in mind can be a clue to look for a more straightforward approach. That’s particularly true of the problems that aim to test your quantitative reasoning ability.

2. Practice working with different forms of numbers.

The GMAT really doesn’t care that much about testing your raw calculating ability. As a result, the test-writers tend to use numbers in the problems that make the math work out nicely. But, you still need to think about the easiest way to do the calculation. For example, if you needed to find 75% of a number, would you multiply by 0.75 or by ¾? If you’re solving a GMAT question, you probably want to choose the fraction because it’s much more likely that you are finding 75% of 400 than 423. 

Read More: GMAT Sentence Correction Tips

3. Use the answer choices for help.

When you solved math problems in school, you probably didn’t have answer choices from which to choose. Teachers tend to care more about the work that you do to solve a problem than the actual answer that you get. The GMAT, of course, cares only that you select the correct answer. By providing answer choices, the GMAT actually gives you more ways to solve the problem. In many cases, you may be able to just test out the answers until you find the one that works.  In other cases, you may realize that there are only one or two answers that even make sense. This kind of question may require no calculations at all if you pay attention to the answer choices!

4. Study the wrong answers.

Remember that the GMAT test-writers study the way that test-takers make mistakes. The GMAT test-writers use that knowledge to come up with wrong answers. In fact, they can increase the difficulty of a problem simply by including more wrong answers that are based on the common mistakes test-takers make when solving a particular problem. So, study the wrong answers! If you can determine what sort of mistake would lead to an included wrong answer, you can use that knowledge towards avoiding those sorts of mistakes on the problem solving questions.

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GMAT Problem-Solving Questions: Tips To Improve Scores

GMAT problem-solving questions in the quantitative section of the GMAT exam can be very challenging. However, if you prepare adequately and ensure that you use your time efficiently and effectively, you will improve your chances of achieving your desired target score in the GMAT exam. This article uses a few examples to create a quick summary of how best to go about finding solutions to problems in this section of your exam.

Let’s take a look at what you need to equip yourself in the process of preparing for this section of your GMAT exam.

What to Expect in GMAT’s Problem-Solving Section

There are two types of questions you’ll come across in the Quantitative Reasoning section of the GMAT exam: Problem-solving questions and data-sufficiency questions. Problem-solving questions make up at least half of the total number of questions you’ll come across in this section. Usually, the quantitative reasoning section contains 31 questions, which means approximately 15 of them will be problem-solving questions.

You will always have five options and one correct selection. The answer choices can be presented as numeric values, variables, or even ranges, and this is going to inform your strategy for solving these problems.

Strategic Implications of the Presentation

Take note of the format of choices in order to select an approach that is efficient and enables savvy mental calculation. For instance, if your answer choices are in the form of fractions, do your mental calculations as fractions, and if you are looking for a range of values, then don’t take a lot of time solving for a specific value. Usually, you’ll have 62 minutes to answer all 31 quantitative questions, which gives an average of 2 minutes per question. However, you have a maximum of 3 minutes for any question because some questions will take you a bit less than two minutes.

Check your pacing after every 10 quantitative questions, as this will help you to avoid clock-watching for every question.  The initial questions matter more according to the scaling of the exam, and, therefore, try to avoid mistakes here and be more methodical. It’s essential to spend a bit of time in this section. For the first 10 questions, spend about 24 minutes total for a ~2:24 average. You can look up after the first 10 questions and see if you have more or less than 38 minutes left.

For the second 10 questions, spend the recommended 2-minute average. This means you have to increase your speed as you go. After these 10 questions, check again to see if you have more or less than 18 minutes left. For the final 11, we are looking at roughly ~1:40 average per question. While you need these questions to complete the section, they don’t have as much impact on your overall score as the previous ones.

A good rule of thumb is to try to guess earlier on questions that you are not sure how to proceed with within the final 11 rather than trying to shortcut everything.

Simple Quantitative Problem-Solving Process

An example of a problem-solving question.

For many years, a surfeit of bears terrorized Yamhill neighborhoods. Then, Bill moved in, and every week he was able to safely relocate the greater of either ⅓ of the bears or 30 bears until a sustainable population of fewer than 30 bears remained in the town. If Yamhill had 270 bears upon Bill’s arrival, what was the number of bears in the sustainable population at the end of Bill’s relocation efforts?

The Problem-Solving Process

1. Set up your scratchpad listing choices vertically from A to E, including simple numbers if provided.

2. Skip to the end of the problem to identify sought values and label your choices as such.

 # Number of Bears at the end of relocation effort =?

3. Read from the beginning taking notes and completing obviously necessary calculations as you go.

• 270 bears at the start
• Relocate Great of ⅓ or 30 bears weekly until < 30 remaining
• \(270-\frac{1}{3}(270)=180\)
• \(180-\frac{1}{3}(180)=120\)
• \(120-\frac{1}{3}(120)=80\)
• \(80-30=50\)
• \(50-30=20\)

So option D is the correct answer.

Complex Quantitative Problem-Solving Question

If x and y are integers, and \(3x+3x+2=10y\), which of the following must be true?

• uppercase roman numerals
• I and III only
• II and III only
• I, II, and III

The Problem Solving process

1. Set up your scratchpad listing choices vertically from A to E.

4. Stop to consider all Four possible problems solving tactics

• Technical Math- Attempt first but abandon quickly if it becomes either not apparent or simple to you. In this case, it is apparent because you have been given the algebraic expression, but if it is not simple to you, then quickly abandon this approach.
• Logical estimation- Attempt at each step of every problem. Constantly eliminate things as much as you can so that when you are in a position where you have to guess, it is from one of two or three rather than from one of five.
• Plugging in value (modeling)
• Plugging in the choices(backsolving)

We can basically use a hybrid of ii-iv in our attempt to solve this problem.

5. Work the problem using your chosen tactic until only one choice is left.

  Note : Don’t fully calculate if not needed. For example, if you know your answer is greater than 6 and is negative, and  -12 is the only option that satisfies those conditions, then just pick -12. 

Always look for opportunities to use logical estimation.

• Note the Roman numeral format
• Which of the following must be true?
• \(3x+3x+2=10y\) (we know that x and y are integers, so we won’t use any fractions here)
• Let us consider the best approach at the moment for us: (a) Use technical math, (b) Plugging in values and Estimation

       5a. \(3x + 3x+2 =10y\)

         \(3x(1 +32) = 10y\)

          \(3x(10) = 10y\)

 This means that: 3x must  = 1, and 10y must = 10.

 x must = 0 (anything to the power of zero = 1) and y must = 1

Option D is the correct answer.

         5b.  If we are not familiar with this math, then we can look at the choices A-E and notice that iii is the most commonly occurring numerical. Then we can plug in x = 0. So if we find out that x cannot = 0 then the answer is A, and we are done.

If we plug in x = 0 then, \(3x(1 +32) = 10y\)

Then 1 0 = 10y is true if \(y = 1\) ( Option D )

In this way, we are able to solve the problem using logical reasoning without needing to know the technical math.

Set up the scratchpad listing the choices vertically from A through E. 

• Include simple numbers with the choices if the numbers are provided
• Note the format of choices to inform tactics and calculation

Skip to the end of the problem and label choices as sought value(s)

• Note if you are seeking a specific or non-specific value 
• Don’t auto-solve for individual values if you seeking a combined value

Read the question from the beginning as you take notes and perform the required calculations 

• If you see a clear path to solving a problem, take it!
• Most “certain but time-consuming” approaches could take you less than three minutes if you start working immediately.

Consider all four possible tactics for the most effective and efficient path to solving a problem at the moment. 

• Technical Mathematics 
• Logical Estimation
• Plugging in values (Modelling)
• Plugging in Choices(Backsolving)

Work the problem using your chosen tactic until only one option remains 

• Always be asking, “I’m I pressing for a solution?” If the answer is “No”, Estimate, Eliminate, Guess, and move on in less than 20 seconds. 
• Allow a maximum of a single calm reread, recalculate, or tactical reset before you must estimate, eliminate or guess 

If a rectangular parking lot with width 4 feet shorter than its length was extended into a square parking lot and doubled its area in the process, what would have been the original length of the parking lot?

Steps 1& 2

We list our choices & skip to the end, and label choices according to what we seek.

Original length

      Length = \(w+4\)

      Original area = \(w(w+4)\) 

      New width = \(w+4\)

      New are = \((w+4)2\)

The area was doubled. Therefore \(w(w+4)=\frac{1}{2}(w+4)2\)

$$w2+4w=\frac{1}{2}(w2+8w+16)$$

$$2w2+8w=w2+8w+16$$

Let’s collect like terms:

$$w2-16=0$$

$$(w+4)(w+4)=0$$

$$w = 4\ \text{or}\ -4$$

 Length cannot be negative, so w = 4

Original length = w+4, = 4+4 = 8(choice C)

If we plug in 8, then

$$\small{\begin{array}{lllll}\text{Original length} & \text{Original width} & \text{Original area} & \text{New width} & \text{New Area} \\ 8 & 4 & 32& 8 & 64=2(32) \\ \end{array}}$$

So option C) is our correct answer through a backsolving approach that might be a lot more straightforward than technical math and saves us quite a bit of time.

Go ahead and do more practice with all the possible tactics, you will get better and find what works for you best.

How Can You Prepare for the GMAT Problem Solving Questions?

GMAT problem-solving questions don’t test advanced mathematical concepts as one might expect. If anything, for most of the questions, you’re required to apply your knowledge of high school math, though this time around, in a more complex and analytical way. That means a little thinking out of the box, and mathematical reasoning should help you solve the problems without much struggle.

That said, here are a few tips that could be of great help in tackling questions in the problem-solving section of your GMAT exams.

Practice doing calculations without a calculator

It’s high time you get used to using scratch paper for calculations and double-checking your work just to make sure there are no errors. You’re not going to use a calculator for GMAT exams. So get used to making basic calculations by hand.

Plugin numbers

It’s essential to plug in real numbers for the variables in the equations so that it’s easy for you to work on the questions without feeling that they’re complex. Along the way, you might find two or more answers that match the numbers you’ve chosen. In such a case, try plugging in new numbers or solving the problem in a different way until you get a correct answer.

Use answer choices to work backward

If you’ve got an idea of where to start, go ahead and plug in an answer to work backward. In that way, you’ll easily eliminate the choices until you arrive at the correct answer. You can start with the middle choice, last, or the first answer in your guesswork. Somehow, you should finally get the correct choice provided you know your way around.

Avoid estimations by all means

When it comes to geometry questions, don’t rely on your eyes in estimating areas, lengths, angle sizes, or any form of measurement. This kind of visual estimation will see you fail in most of the questions, and this will affect your overall score.

Start with what you know

Keep in mind that GMAT exams will only require you to use high school-level math to answer the questions. Therefore, it’s advisable to start small on the questions by using what you know and break the problem into small steps that you can achieve with the little knowledge you have. In that way, you’ll be able to work towards an answer. 

Use high-quality study materials

The best way to prepare for your GMAT exams is by using real problem-solving practice questions from past exams or questions that specifically follow the GMAT format. At AnalystPrep , we provide lots of study resources for all the sections of your GMAT exams. You can get a GMAT study package with thousands of real problem-solving practice questions to help you prepare for your exams adequately. It’s a one-time investment that will see you improve your GMAT scores and consequently hit your targets.

GMAT problem-solving questions aren’t as hard as you can imagine. All you need to do is to practice adequately for the exams and brace yourself for the exams.

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GMAT Problem Solving—Be Flexible in Your Approach (and Know What You Need to Know)!

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Probably the most common misconception about the GMAT is that the quant section is a “math test.” Obviously, math skills are essential to success and your fluency with underlying math concepts directly affects your score. However, the problems in the quant section are testing much more than math:

• Who is good at creative problem solving?
• Who can deal with abstract presentation of simple concepts?
• Who leverages every resource and hint in a problem?
• Who reads carefully and follows instructions properly?

Of all the question types on the GMAT, test prep companies feel most comfortable creating unofficial quant problems. They hire math whizzes to crank out content questions and consumers gobble them up in their preparation for this section.

While these questions will help with content improvement, they usually lack the type of difficulty you see in a full 75% of the quant questions on the GMAT! By using mainly official Problem Solving questions, you not only improve your understanding of underlying content but also prepare yourself for the other types of difficulty that plague a majority of students on hard quant questions.

Best Practices for GMAT Problem Solving Questions

On the quant section of the GMAT, it is helpful to think of Problem Solving questions in two categories:

Type 1 : These questions are more just math questions and require you to apply conceptual knowledge and practical math approaches to solve a question.

Type 2 : These questions are made difficult by abstract presentation, complex or tricky wording, red herrings, your choice of approach—i.e. those in which just understanding the math will not get you to the correct answer efficiently (if at all!).

Type 2 questions have always been the mainstay of the quant section on the GMAT, and these questions are what make the test so hard for students. To explain this type of question, I have always used this example:  on the exam, GMAT test writers turn 1 + 1 into a 90 th percentile problem by making it exceptionally hard to sort through all the garbage and see that you just need to do a simple addition. When you miss this question, you don’t need to go do more addition drills, you need to learn how to sort through abstract presentation and deal with complex wording! People do not spend enough time improving these types of skills that are so essential on hard official quant questions.

In the shift to the GMAT Focus exam, I expected to see even fewer Type 1 questions but so far this has NOT been the case. Anecdotally, I would say that ¼ of the questions fall into category 1 and ¾ fall into category 2 on the new exam, the same proportion as on the legacy version of the GMAT.

This is still a small percentage of the quant questions overall, but you should think of these Type 1 questions as gifts on the GMAT quant section:  if you do the proper prep and understand the math, you will get these questions correct with little effort. It is also important to note that the standard for solving pure math questions around the globe is very high. If it is mostly just a math question, you really need to get it right to be competitive on the GMAT quant section.

So, when I review missed questions with students and I see that they are missing a Type 1 question, I say: “Know What you Need to Know! and this question would feel easy.”   There is no better example of this than the first question covered in this section, a question I see far too many students miss.

GMAT Problem Solving: Example Question #1

Detailed Explanation For Question 1

This process is made more difficult in this official question with two mechanisms:

• The denominator does not just contain individual terms with roots but also integers or multiple roots added together. This makes for a more difficult version of rationalizing the denominator in which you must recognize the difference of squares and” multiply by one” using the conjugate of the denominator. Even though this is harder, these are both core best practices that you learned in algebra in high school and that you must know for the GMAT. This skill has been tested so many times on the GMAT that you should recognize two things immediately: you should use the conjugate and the denominators will simply disappear with the numbers they have used.
• Three terms with roots in the denominator are being added together, so the test-maker entices students to try to find a common denominator or take some other incorrect approach.

The important point with a manipulation like this is that you simply must recognize what to do! We cover these types of important math skills in detail in our Refresh Modules and then you need to practice them with questions like this. Once you see what to do on the first term, then just do the same type of manipulation on each fraction individually and add the simplified terms together.

With each of the three fractions simplified and the denominators disappearing, you are simply adding together the following three terms:

The correct Answer is thus (E).

While these three steps look tedious on paper, the reality is that a lot of people taking the GMAT are going immediately to the last step shown above without any written work. You want to be one of those people!

If you don’t know what to do on this problem algebraically (and the point of this example is that you should!), it is important to note that this question can also be solved cleverly using answer choices and simply estimating the roots. Since the first four answer choices are all less than 1/2, you know the answer must be (E). Estimating the two roots in the question stem allows you to see that the sum of the three expressions will get close to 1, and none of the other answers are close. If you solved this question with this technique, good for you! However, this question could easily contain 6/7 as an answer, and then you would be in trouble.

As you prepare for the exam, pay special attention to any misses on questions like this that just require math knowledge. They are easier to prepare for and it is important that you get them right. With difficult abstract problems involving lots of red herrings or tricky wording, you simply can’t get win them all, but for these types of questions, you can develop complete mastery.

GMAT Problem Solving: Example Question #2

One year ago, a window washing service charged $100 for setup and an additional $30 per hour for on-site washing. This year the company charges $20 for setup and an additional $50 per hour for on-site washing. Which of the following is equivalent to the percentage change from last year to this year that the company charges for setup and x hours of on-site washing?

Detailed Explanation For Question 2

This example is a classic type 2 question—it feels abstract and you must read carefully. You can be comfortable with most percent questions on the GMAT and still get this wrong (or waste a lot of time) if you don’t choose the right approach.

If you search the internet for explanations on this question, you see everyone explaining one tedious algebra step after another AND you see many people who have either botched that algebra or made a mistake setting up the percent change. In 20 years of preparing people for the test, I have only seen a few variable-in-answer choice percent questions for which algebra was a better approach than number picking. Here the algebra is not as tedious as in other questions of this kind, but number picking is unquestionably easier.

As a best practice for the exam, always take a little time to decide on your approach (algebra, conceptual thinking, backsolving, or number picking) before jumping into a question. Don’t swim upstream with a long math approach when you can take advantage of answers or use your own numbers. As we teach in our curriculum, whenever you see percent change questions with variables, try number picking first and only go to algebra if that is not working. When number picking, it is important that you are careful with the number(s) that you choose for variables—that is, anticipate and use numbers that will make solving the question as easy as possible. On harder number picking questions, you may choose the wrong numbers first and only realize which ones will work better as you move into the question.

The final step after you solve with the number(s) you have chosen is to plug that number into each answer, looking for your solution, in this case 8%. By plugging 5 into each answer, it is clear that (D) and (E) are wrong as they would be negative. (A) is way too big and (C) would leave 27 in the denominator (i.e. not reduce to 8) so the correct answer must be (B).

Thinking about this question broadly, it is really quite simple with number picking as long as you pick a good number!!!! One risk in number picking is that you get buried in awkward calculations. Imagine if you picked say 3 or 7 for x. With 3, you would be starting at $190 and calculating the % change to $170. Ugly. With 7 it would be $310 to $370. Also, ugly.

Number picking is an essential strategy for GMAT word problems with variables in answers and for many other question types (percent questions or others in which the starting number can be anything). You must practice and hone this strategy in the same way that you do with certain quant skills and calculations, but most people are not doing that in their preparation. As you move through official questions, take the time to consider alternative approaches after you have solved a question, particularly if your method seemed tedious or time-consuming. As a final exercise, think about how easy you can make a problem like this compared to how it first seems:  if I asked you what the percent change was from 250 to 270, I am confident that all of you could get it correct in less than a minute!

Caution: Avoid Unofficial GMAT Problem Solving Questions (except when you need content help)

Utilizing unofficial Problem Solving questions is not as worrisome as using unofficial Verbal or Data Insights questions, which can actively hurt your score. Since most unofficial Problem Solving questions are more just about the math, they can help improve your mastery of underlying math content.

With that being said, you better move to official questions early in your preparation once your content knowledge is solid. Without using the complex and cleverly made official quant questions, you are not preparing for the more complicated problems in which you must sort through clever wording, use answer choices actively, number pick to simplify the problem, etc. People with strong quant skills (engineers, math majors, etc.) are often surprised that their quant scores are not higher, and it is often because they are not prepared for this “Type 2” difficulty that appears in a majority of quant questions on the GMAT.

To strengthen your skills and tackle these “Type 2” difficulty questions with confidence, consider joining our live GMAT prep course . These sessions are designed to guide you through the complexities of official quant questions in a supportive, interactive environment.

Questions about this article? Email us or leave a comment below.

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GMAT Prep Online Guides and Tips

Gmat math tricks: the 9 best tips and shortcuts.

Luckily, this means that there are several GMAT math tricks, tips, and shortcuts that you can use to improve your performance. In this post, we’ll give you all the major GMAT quant tricks, including tips and shortcuts for each of the two question types as well as some that apply to both. With these GMAT math tricks in your arsenal—plus the boatloads of studying you’re surely doing—you’ll be well prepared to nail the Quant section on test day.

GMAT Math Tricks: What Can They Help You With?

The makers of the GMAT will tell you that there are no such things as “tips” or “tricks” for doing well on the Quant section. Unfortunately, there is some truth to this: while GMAT math tricks can help you a little bit, the only real way to ace the GMAT Quant Section is to invest lots of time in focused, targeted preparation. Yep, that means study, study, study.

That said, each of the GMAT quant tricks below are extremely useful. Some help you execute basic calculations (like multiplication and division with unwieldy numbers) more quickly and efficiently; some help you get to the right answer without even having to solve the equation. Additionally, many of these GMAT Quant tricks are particularly helpful for guessing strategically on questions you’re stuck on —so when all else fails, you can feel like you have a solid plan and a fighting chance to get the right answer.

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General GMAT Math Tricks

Below are some overall GMAT Quant tricks—as in, tips and shortcuts that apply to both question types.

#1: Simplify Calculations with Multiples of 10

Working with multiples of 10 is easy in addition, subtraction, multiplication and division. Even when you’re given a less pretty number, you can still use multiples of 10 to solve it painlessly.

Addition and Subtraction with 10

To add two and three digit numbers that aren’t already a multiple of 10 or 100, round the number to the nearest 10s or 100s digit, do the addition, and then add or subtract the result by the number you rounded off. Do the opposite when subtracting.

$$525 + 311$$ $$= 500 + 311 + 25$$ $$= 811 + 25$$ $$= 836$$

Multiplying and Dividing with 10 via the Distributive Property

To multiply by an awkward number, such as 16, you can multiply first by 10, and then multiply by 6, and then add the two products together:

$$n × 16 = (n × 10) + (n × 6)$$

You may remember that the rule that applies to this calculation is called the distributive property , and it works as follows:

$$a (b+c) = (a × b) + (a × c)$$

This works for subtraction as well:

$$a (b – c) = (a × b) – (a × c)$$

Here’s a full example:

$$5 × 37 = 5 × (40 – 3)$$ $$= (5 × 40) – (5 × 3)$$ $$= (200) – (15)$$ $$= 185$$

The distributive property is one of the most helpful tools in your GMAT toolkit because it simplifies unwieldy calculations.

Multiplying and Dividing between 11 and 19 via 10

There’s a slightly different trick for multiplying any two numbers between 11 and 19. Here, you can add the ones digit of one number to the other number, multiply that result by 10, and then add the product of just the ones digits.

Here’s an example:

$$11 × 17 = (18 × 10) + (1 × 7) = 187$$

Squaring between 11 and 19 via 10

To square any number $n$ between 11 and 99, find the nearest multiple of 10, and then find out how much you would have to add or subtract to get there. We’ll call the value that you’d have to add or subtract to get to a multiple of 10 $d$, for “difference.”

Next, do the opposite function with $d$ and the original number $n$ (add it if you had to initially subtract it to get to a multiple of 10, subtract if you had to add) to get two numbers that average out to $n$ ($n$ + $d$ and $n$ – $d$).

Finally, multiply those two numbers and add the square of $d$.

$$57^2 = (60 × 54) + 3^2$$ $$57^2 = (60 × 54) + 9$$ $$57^2 = (10 × 6 × 54 ) + 9$$ $$57^2 = 3240 + 9 = 3249$$

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Little GMAT math tricks like the above make mental math faster and easier, which is key to success on the Quant section, as you don’t have access to a calculator.

#2: Plug in Numbers, but With Care

Many GMAT Quant questions don’t require you to solve all of the many equations embedded within them. Sometimes picking a simple number and substituting it for the unknown variable works even better—and makes the problem simpler and easier—than actually solving the complex algebraic equation.

For problem solving questions— especially when you’re looking for a rate, ratio, fraction, or percentage of an unknown whole —picking a value to stand in for the unknown can save time and make it much easier to visualize and solve the problem.

Here’s an example problem solving question that shows this strategy in action:

To practice law in their state, the third year law students at Western University have to pass the bar examination. If ⅓ of the class opted not to take the bar examination and ¼ of those who did take the test, did so and failed. What percent of the 3Ls will be able to practice law in their state?

This question provides a perfect use case for plugging in numbers. Since we’re dealing with ⅓ and ¼, you should choose a number that both 3 and 4 factor into neatly. So let’s go with 12, the lowest common multiple.

If the class has 12 people in it and ⅓ don’t take the test, that means 4 don’t take it and 8 do. Of those 8 who did take the test, 2 fail, so 6 in total are able to practice. The answer is asking for the percentage, which is now easy: 6/12 is ½, or 50%.

For data sufficiency questions, however, plugging in numbers is only really helpful for proving that a statement is insufficient. The reverse is much more time consuming, and so it doesn’t make sense over solving the problem, so only resort to it if you strongly suspect that a given statement isn’t sufficient and you don’t know another way to proceed.

Here’s an example of this strategy in action in a data-sufficiency-style question (with just one statement, for the purposes of illustrating number-picking):

If integer $n$ is greater than 1, is 2 $n$ – 1 prime? 1) $n$ is even

For this first statement, let’s plug in some even values for $n$:

Try $n$ = 2. We get 2 $n$ – 1 = 2 2 – 1 = 3, and 3 is prime.

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So far so good, but now try $n$ = 4. We get 2 $n$ – 1 = 2 4 – 1 = 15, and 15 is not prime. So statement 1 is not sufficient.

4 Tips for Picking Numbers

Here are four tips for picking numbers effectively and avoiding common traps in both question types:

1. Make sure that the number you pick meets all of the conditions in the question.

Note that some of the conditions may not be stated in their “official” terms, so you’ll have to read into the given information to recognize the rules at play. For example, a question stem might tell you that a given number y “has only two factors.” This means that y has to be a prime number. This is yet another example of how the math itself isn’t all that hard on the GMAT—what’s hard is uncovering the buried information that the question stem is masking by putting it in unusual words.

2. Be careful to avoid making assumptions beyond the given conditions. 

For example, if your question states that $a$, $b$, and $c$ are consecutive numbers, you can’t then assume that $a$<$b$<$c$ or that $a$>$b$>$c$. All you know is that they are consecutive—you don’t know the exact order in which they each occur.

Another example is if the question states that $x$ > 5. Many would assume that the number has to be 6 or higher. But unless it is stated that $x$ must be an integer or a whole number, then we can’t make this assumption, as there are an infinite number of decimal values between 5 and 6.

Assuming that the answer is a whole number without being told is a mistake people make all the time on the GMAT.

3. Avoid a number that represents a possible exception to the general rules of a condition.

For example, 2 is the only even prime number and can lead to some confounding results when worked with in an equation, so you may not want to choose it as your “plug-able” number in a prime numbers question.

4. Plug in numbers that are easy to work with.

Don’t use a crazy number like 367—the whole point is to make the problem simpler! As long as they meet all the rules of the conditions given (and don’t have their own confounding special properties), simple numbers like 3, 4, 5, etc. should be fine.

GMAT Data Sufficiency Tricks

Data sufficiency questions are tough for everyone at first, since they’re stylistically different from the math problems you’re used to doing. Once you get used to them, however, you can discern some tricks and shortcuts that are baked into the unique format of these peculiar questions. Below are the best GMAT data sufficiency tricks.

#1: Work Methodically Through the Choices

With their unchanging list of answer options, data sufficiency questions lend themselves perfectly to a special kind of process of elimination: You should always work through the answer choices in the same order.

We’ve pasted the choices below for your review. As soon as possible, you should memorize these answer choices until you know them cold—this will save you a good deal of time on the test. Note that they won’t come with A-E lettering on the real thing (we’ve put that in to make referring to them easier); instead, they’ll each have a bubble to the left that you’ll click on to indicate the answer.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

D. EACH statement ALONE is sufficient to answer the question asked.

E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

First: test statement 1. If it isn’t sufficient to find one and only one answer, then eliminate (A) and (D). If it is sufficient, eliminate (B), (C), and (E).

Next, test statement 2. If it isn’t sufficient and statement 1 was sufficient, then (A) is the answer. If it is sufficient and statement 1 was also sufficient, then (D) is the answer. If it is sufficient and statement 1 wasn’t sufficient, then (B) is the answer.

If it isn’t sufficient and statement 1 also wasn’t sufficient, then either (E) or (C) is the answer.

You should only put the statements together if, after testing each statement for sufficiency by itself and going through the process of elimination above, both statements are insufficient and you’re left with (E) and (C). At this point, there are only two options: either they’re sufficient when taken together, or they’re not. If putting them together gets to only one answer, then (C) is the answer. If not, then (E) is the answer.

#2: You Don’t Always Have to Solve Questions All the Way

Very often, you don’t necessarily have to determine the value of the expression in the data sufficiency question prompt or in the statements: Your task is simply to determine if the information provided is each statement is enough to do so.

For example, let’s say you get the DS question stem: “What is the value of $x$?” (This is a fairly common type of DS stem.) And let’s say you’re given the following in statement 1:

Statement 1: 22$x$ + 251 = 550

Being the studious person that you are, you might be tempted to solve for $x$ in statement 1 by subtracting 251 from both sides, and then solving for $x$ by dividing by 22 (which is tricky, since it doesn’t result in a whole number). But you don’t actually need to solve for $x$ : Just by looking at the equation, you know that statement 1 can lead to only one possible value for $x$, so it is sufficient to determine the value of $x$, as asked.

Already, you can eliminate (B), (C), and (E)—and you didn’t even need to “do” any math!

#3: Use the “$n$ Variables, $n$ Equations” Rule

Data sufficiency questions that ask you to solve for one variable often feature two variables (usually $x$ and $y$) in the statements. Remember the “$n$ variables, $n$ equations” rule of linear equations for these questions: you need $n$ distinct equations to solve for $n$ variables; thus to solve for $x$ and $y$, you need two distinct equations that include both $x$ and $y$.

This means that statement 1 alone is usually not sufficient, so you can eliminate (A) and (D) after a quick glance to make sure that’s true. However, don’t just pick (C) and move on: You must simplify each equation to double-check that one isn’t the same as the other.

Here’s a brief example:

What is the value of $x$? Statement 1: 8$y$ = 12 – 4$x$ Statement 2: 2$x$ + 4$y$ = 6

Both of these equations are the same, so you can’t solve for one variable by plugging in its equivalent expression of the other:

$x$ + 2$y$ = 3 $x$ = (3 – 2$y$) 2(3 – 2$y$) + 4$y$ = 6 6 – 4$y$ + 4$y$ = 6 6 = 6 $y$ = ?

As long as there are two distinct equations with $x$ and $y$ (and there are no squared variables, which we’ll get into below), then both statements together should be sufficient

#4: Avoid the Square Root Trap

If $x$ 2 is any positive number, then $x$ could be a positive number or a negative number, as a negative times a negative results in a positive as well. This means that there are two possible values for $x$, one negative and one positive. Assuming that “$x$ 2 = [any positive number]” provides sufficiency to get to one value of $x$ is a very common mistake, but it’s easy to avoid by simply remembering this rule!

GMAT Problem Solving Tricks

GMAT problem solving questions are often thornier than they appear. Below are the best GMAT math trick, tips and shortcuts to help you strategically approach even the toughest problem solving questions.

#1: Look at All the Answer Choices Before Solving

This is generally a better strategy than to solve the problem right away and then look for a choice that matches your solution, as the choices themselves can provide clues to how to solve the problem—especially if there’s a property or shortcut that can help you do so. As always, the GMAT almost never requires you to do extremely laborious equations out by hand—they want to see that you can get to the right answer efficiently (as an excellent business person would)!

#2: Estimate to Cross off Wildly Wrong Answers

On a related note, many problem-solving questions test your ability to approximate reasonably, rather than precisely solving a complicated equation.

For example, let’s say you have to multiply a given number by a strange fraction, such a 11/53. This is fairly close to ⅕, or .2. The GMAT wants you to get to the right answer efficiently: they don’t want you to do all the work of dividing the given number by 53 and then multiplying by 11 on your scratchpad. It’s highly likely that the wrong answer choices will be far away from about ⅕ of the number, with only one choice that’s even in the ballpark.

Alternatively, you may get a question that appears to ask you to multiply many large numbers together, but the answer choices are all in exponent form and are all an order of magnitude away. In this case, you might be able to just estimate and find the closest answer as well.

Here’s an example of a good problem solving question to use estimation on:

James Woods High School’s senior class has 160 boys and 200 girls. If 75% of the boys and 84% of the girls plan to attend beauty school, what percentage of the total class plan to attend beauty school?

The first thing to note is that 84% is an unwieldy number. When you see figures like that, it’s a sign that you may want to look for an estimating shortcut.

So what can we eyeball? Since there are 20% more girls than boys, we know that the weighted average will be closer to the girls’ percent than the boys’ percent . So we should look at the answer choices to see what we can already get rid of.  We can easily eliminate A, since 75% is going to be too low to be the weighted average. We can also cross out D and E, since they will both be too high (and are essentially equal).

79.5%, as the unweighted average of 75% and 84%, is the low extreme—the right answer will be slightly higher than that when adjusted for the total number of boys and girls, but just by a little bit, since there’s not a drastic difference in number between the two groups. So C, at 80%, looks right just by estimating. C is in fact the correct answer.

#3: Backsolve

Rather than plugging in numbers of your own choosing, some problem solving questions can be solved by working backward: plug the answer choices in, do the equation(s) with them, and cross off the choices that don’t balance. Usually there’s a faster way to get to the right answer, but this method can be a lifesaver when you really just don’t know how else to solve a given question.

The best way to approach backsolving is to start with C: the value that’s in the middle of all the choices . This way, even if it doesn’t balance the equation, you can determine whether the number that will work will be higher or lower (and rule out the higher or lower answer choices accordingly).

Here’s an example of a problem solving question that lends itself to backsolving:

What is the smallest positive integer $x$ for which $x$ 3 + 5$x$ is more than 80?

A. 2 B. 3 C. 4 D. 5 E. 6

As always when backsolving, start with C, $x$ = 4.

$$4^3 + 5(4) = 64 + 20 = 84$$

This is just over 80, so C could be the answer and, even if not, we can already eliminate D and E. Our powers of estimation tell us that 2 (A) is definitely going to yield a result far below 80, so let’s just check that 3 (B) doesn’t work:

$$3^3 + 5(3) = 27 + 15 = 42$$

That’s below 80, so $x$ = 4 is the smallest possible integer that satisfies the condition and C is the answer.

In Conclusion: Summary of GMAT Math Tricks

Simplify unwieldy calculations with the distributive property and other other tricks that allow you to do basic arithmetic with easy numbers like 10. Plugging in numbers is a great strategy for when you can’t think of another way to solve the equation , but be careful with the numbers that you choose. Plugging in numbers works best to prove insufficiency for data sufficiency questions, but it may make more sense to backsolve for problem solving questions.

You can “game” data sufficiency questions by working methodically through the answer choices , and remember that you don’t always have to solve or “do out” a complex equation to prove sufficiency. And  if you encounter two variables on a data sufficiency problem, you  will need two equations to solve for both of them.

Avoid traps by remember that positive squares can have positive or negative square roots, and by not presuming a number is an integer unless told.

For problem solving questions, look at the answer choices before solving the problem.  Once you’ve identified what the question is asking of you,  estimate to cross off answers that can’t possibly work . Sometimes estimating will get you all the way to the right answer. Finally, don’t be afraid to backsolve —but always start with C , or the middle value, when doing so.

What’s Next?

Check out our guide to  10 tips to master the quant section .

When you’re ready to conquer the subject areas tested, check out our GMAT-specific guides to  integer properties , geometry formulas , and  rate problems .

If you need help getting started and developing a study plan, we’ve got you covered there too .

Happy prepping!

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Author: Jess Hendel

Jess Hendel is a Brooklyn-based academic advisor, test prep tutor, and content writer for PrepScholar. A graduate of Amherst College, she has several years of experience writing content and designing curricula for the top e-learning organizations. She is passionate about leveraging new media and technology to help students around the world achieve their potential. View all posts by Jess Hendel

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Sample GMAT Problem Solving Questions

We’ve already covered why studying with official practice questions is the best way to prepare for the GMAT .  But even if you come up with the correct answer to an official problem, you still might not understand the underlying principles used to create that particular question, leaving yourself open to traps and pitfalls set by the test writers.  In the explanations below, I will use some of the core tenets of the Menlo Coaching GMAT curriculum to breakdown two official GMAT problem solving questions and provide important principles for correctly attacking this question type in the future. 

Multiple choice “problem solving” questions are, to most students, familiar, yet they generally do not approach them properly. To succeed on these questions, you obviously need the requisite knowledge related to the content area being tested—math skills related to arithmetic, algebra, etc. However, it is just as important to read carefully, leverage every hint, and choose the right strategy (backsolving, number picking, conceptual thinking, etc.) People think of multiple-choice problem solving questions as just plain math questions, but this GMAT sample question shows that they are much more than that. Take a look at the following questions, and check out our problem solving video below.

GMAT Problem Solving, Sample Question #1

Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?

GMAT Problem Solving, Sample Question #2

A certain airline’s fleet consisted of 60 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the type A planes and acquired 4 new type B planes. How many years did it take before the number of type A planes left in the airline’s fleet was less than 50 percent of the fleet?

Sample GMAT Questions by Topic

• Data Sufficiency: Practice for the GMAT with Official Data Sufficiency Sample Questions
• Data Insights: How to Approach Data Insights: Practice Questions and Explanations
• Reading Comprehension: How GMAT Reading Comprehension Questions Mislead Test Takers: Practice Questions and Explanations
• Critical Reasoning: How to Succeed Against Official GMAT Critical Reasoning Questions

Need even more problem solving help? Read our guest post on MBA.com to learn why, in GMAT problem solving, flexibility is key! Plus, practice with more official GMAT problem solving questions from Poets&Quants.

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Home » Free GMAT Prep » GMAT Problem Solving Questions and Tips

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GMAT Problem Solving Questions and Tips

Wondering how to tackle problem-solving questions on the GMAT? The good news is that the questions asked in the GMAT are similar to the math problems you’ve been dealing with throughout your schooling years. However, a quick review of the basics might be required to help you get right back on track and start acing the GMAT quant section. Read this article to learn more about GMAT problem-solving questions. 

Before we begin, let us understand what the GMAT quant section is all about.

GMAT Quantitative Reasoning

The Quantitative Reasoning is a 60-minute-long section on the GMAT exam dedicated to quantitative problems. Throughout the GMAT Quant Section, you will have to answer a total of 31 questions within the 60-minute duration. Furthermore, the quant section is scored on a scale of 6-51 with a single point increment. 

Wondering if you need to be a pro at maths to ace the GMAT quant section? Not really! However, you may need to master the basic concepts to solve the questions of various difficulty levels. The GMAT does not expect you to be an expert in mathematics. Using computer-adaptive difficulty, the algorithm that gauges your ability to answer a question of a certain difficulty level, the GMAT tests you with questions of an elementary level. Hence, the stronger you’re with the basics of the GMAT Quant the better you’ll perform on the quant section of the test.

Now that we know what the GMAT Quant section is, let us understand what GMAT problem-solving questions are like and how to approach them.

GMAT Quant Mean, Median, & Mode questions

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GMAT Mean, Median, & Mode solutions

GMAT Problem Solving Questions

The GMAT quant section comprises two types of questions: Data Sufficiency and Problem-Solving. Data sufficiency questions provide you with a statement along with two supporting pieces of information and you will have to answer if the data provided is sufficient or not to arrive at the correct answer to the question presented. On the other hand, problem-solving questions require you to use the information available and select the correct answer from the five multiple choices provided.

An example of a GMAT problem-solving question is as follows:

In a certain office, the ratio of smokers to non-smokers is 4:5, then approximately what percent of the employees in the office were non-smokers?

The GMAT problem-solving question is based on the following topics:

• Distance, rate and time
• Permutation and combinations
• Factors and prime factorization
• Problems with averages
• Estimation questions
• Difficult dice questions
• Difference of two squares
• Work and work rate
• Circle and line diagrams
• Set problems with Venn diagrams
• Scale factor and percentage change
• Standard deviation 
• Function notation
• Algebraic Factoring
• Hard factorial problems
• Back solving from the answers
• Distance in x-y plane
• Line in the x-y plane
• Tricks and calculating combinations
• Parallel and perpendicular lines and midpoints in the x-y plane
• Probability: And, Or rules
• Probability: At least statements
• Probability: Counting problems
• Hard counting problems
• Probability: Geometric probability

GMAT Problem Solving Strategies

Here are a few GMAT problem-solving strategies you should adopt to approach each problem-solving question on the test.

• Be quick and don’t spend too much time reading a question. Most times GMAT questions are framed to trick you into spending too much time reading the question.
• Although you need to be quick, try reading the question carefully. Hence, you have to be quick and careful at the same time to not miss out on essential cues to solve the problem.
• Use the plug-in strategy by going through the answers and plugging in each of the answers to help solve the question.
• Don’t waste time if you can’t solve the question. Time saved on one question by guessing an answer can be spent on solving another question that you may be stronger at.

Mistakes to avoid when solving Problem Solving Questions

Here are a few common mistakes test-takers make while solving problem-solving questions that you can learn and avoid.

• Getting lost in the information shared. Often, a lot of extraneous data will be given in the question and you need to filter through it to pick out only what’s relevant.
• Missing negative signs in equations, especially when you move terms from left to right and vice versa.
• Trying to use algebra to solve questions, when plugging in numbers is a far simpler approach.
• Not using deductive reasoning to eliminate incorrect answer choices.

Now that we have mentioned to you about GMAT problem-solving questions, the topics covered and strategies you should adopt, you’re better positioned to enhance your GMAT practice.  

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GMAT Problem Solving Questions

Last Updated on November 27, 2023

Whether you are taking the current version of the GMAT or the new GMAT Focus, GMAT Problem Solving questions are the majority of the GMAT quant questions you will see. Thus, to get a great score on the GMAT, you must be able to crush this question type. In this blog, we will discuss the essence of GMAT Problem Solving questions and look at some GMAT Problem Solving sample questions and their solutions. (If you need data sufficiency help, we’ve covered that in a separate article .) If you need more practice after completing what we offer in this article, please check out the Target Test Prep online GMAT course .

Here are the topics we’ll cover:

What is a gmat problem solving question, the gmat quant topics.

• GMAT Problem Solving Example 1
• GMAT Problem Solving Example 2
• GMAT Problem Solving Example 3
• GMAT Problem Solving Example 4

GMAT Problem Solving Example 5

What’s next.

Let’s begin with a discussion of what a GMAT Problem Solving question is.

The good news is that GMAT Problem Solving questions are identical to the multiple-choice questions you’ve seen since your days of doing basic math questions. As such, a Problem Solving (PS) question presents the answer choices A, B, C, D, E and has just one correct answer. On the current version of the exam, PS questions make up about two-thirds of the questions in the GMAT quantitative section. So, you’ll see about 21 PS questions.

On the GMAT Focus, PS questions are actually their own section, which consists of 21 GMAT math questions. So, whether you are taking the traditional GMAT or GMAT Focus, you need to know GMAT Problem Solving questions!

There are 21 Problem Solving questions on GMAT Focus and around 21 Problem Solving questions on the standard GMAT.

Now, let’s discuss the quant topics you may see covered in GMAT Problem Solving questions.

If you are somewhat new to the exam, you may wonder, what the heck is tested in the GMAT quant section? Most of what is tested on the GMAT is math that you likely saw at one time in your life. So, rather than learning things from scratch, you can build back up the quant muscles you previously had. Sure, those concepts are tested slightly differently on the GMAT, but in general, there should not be many math topics that are completely new to you.

There is a high likelihood that you are familiar with most of the math topics tested on the GMAT.

Let’s list the topics tested:

• GMAT Arithmetic Questions
• Fractions and Decimals
• Number Properties
• GMAT Algebra Problems
• Quadratic Equations
• GMAT Number Properties
• Exponents and Roots
• Inequalities
• Absolute Values
• Word Problems
• Rate Problems
• Work Problems
• Unit Conversions
• Ratios and Proportions
• Overlapping Sets
• Permutations and Combinations
• Probability
• GMAT Geometry Questions
• Coordinate Geometry

Note that Geometry is not included in the GMAT Focus.

Now that we are familiar with the basics of a GMAT Problem Solving question and the topics those questions may involve, let’s get into our GMAT problem-solving practice.

In the sections that follow, we will first present a topic, and then show how it can be presented in a GMAT PS question.

GMAT Problem Solving Topic 1: Number Properties – Factorial Divisibility

The first example is based on the topic of factorial divisibility, which is one of many integer properties. The nice thing about factorial divisibility is that, although it appears to be a difficult topic, it’s actually quite simple once we learn to use a very cool strategy for this type of question.

For example, let’s say you need to determine the maximum value of n for the expression (14!) / (2^n) such that the result is an integer. To determine the max value of n, we do the following:

First, divide 14 by 2, and note the quotient while ignoring any remainder:

14/2 has a quotient of 7.

Next, divide 14 by 2^2 = 4, and note the quotient while ignoring any remainder:

14/4 has a quotient of 3.

Next, divide 14 by 2^3 = 8, and note the quotient while ignoring any remainder:

14/8 has a quotient of 1.

Next, divide 14 by 2^4 = 16, and note the quotient while ignoring any remainder:

14/16 has a quotient of 0.

Since we have found a quotient of zero, we can stop. The final step is to add up all the quotients; that sum is the maximum value of n. So, the maximum value of n is 7 + 3 + 1 = 11.

Use the strategy provided above to solve factorial divisibility problems.

Let’s practice with an example.

GMAT Problem Solving Example 1:

What is the greatest integer j, such that 240! / 4^j is an integer?

First, we divide 240 by 4^1, noting the quotient and ignoring the remainder:

240 / 4 = 60

Now we divide the quotient 60 by 4^2, noting the quotient and ignoring the remainder:

60 / 4^2 = 60 / 16 = 3

Now we divide the quotient 3 by 4^3, noting the quotient and ignoring the remainder:

3 / 4^3 = 3 / 64 = 0

Because the quotient is 0, we stop.

The value of j is the sum of all the quotients, so we have:

60 + 3 + 0 = 63

This tells us that there are 63 fours in 240!

Thus, we know that the largest value of j that allows 240! / 4^j to be an integer is j = 63.

Next, let’s discuss a topic from inequalities.

GMAT Problem Solving Topic 2: Inequalities – Combining Equations and Inequalities

One of the first things you will learn on the GMAT is solving for the value of the two variables contained in two equations, you often use the substitution method, which functions just as it sounds like it would. We also use this process when we have one equation and one inequality containing two variables.

For example, let’s say we have the following:

Equation: y = 2x – 1

Inequality: 3x + 4y > 25

If we want to know what is true about x, we do the following:

Since y = 2x – 1, we can substitute 2x – 1 for y in the inequality 2x + 4y > 25. Doing so gives us:

2x + 4(2x – 1) > 25

2x + 8x – 4 > 25

10x > 29

x > 29/10

Thus, we know that x is greater than 2.9.

When working with inequalities and equations, we can substitute the equation into the inequality.

Let’s practice with one more example.

GMAT Problem Solving Example 2:

If 2x – 4y = -10 and 5x – 3y < 3, then which of the following must be true?

• y < 28 / 13
• y < 53 / 17
• y > -28 / 13

The answer choices indicate that we need to get an answer for y, so we will first solve the equality to get x in terms of y.

2x – 4y = -10

2x = 4y – 10

x = 2y – 5

We now substitute 2y – 5 for x into the inequality and solve for y:

5(2y – 5) – 3y < 3

10y – 25 – 3y < 3

GMAT Problem Solving Topic 3: Rates – Converging Rate Questions

As you study rates on the GMAT, you will discover that there are many ways in which rate questions may be presented. Thus, you’ll want to become familiar with each type and know the associated formula for each one. If you can apply the appropriate GMAT math strategies to rate questions, you’ll be in a great place come test day.

We do not have the time to cover each type of rate question in this article, but we will focus on a common type, the converging rate question.

A converging rate is when two people or things head toward each other on a parallel path. An important characteristic of converging rates is that when two objects converge (or meet), the total distance that originated between them is equal to the sum of the individual distances of the two objects. Thus, we use the following formula:

Distance of Object 1 + Distance of Object 2 = Total Distance Traveled

When two objects meet, the sum of their individual distances is equal to the total distance they traveled from their respective starting points.

Let’s practice how we would use this formula with an example.

GMAT Problem Solving Example 3:

The distance between Philadelphia and Boston by train is 311 miles. Train A departs Philadelphia at 12:00 PM, traveling to Boston at a constant speed of 50 miles per hour. Train B departs Boston at 12:30 PM and heads toward Philadelphia on a parallel track at a constant speed of 60 miles per hour. How far has Train A traveled at the moment the trains meet?

We see that this is a converging rate question, as two trains are traveling toward each other (on parallel tracks!).

Let’s let r1 = Train A’s rate, t1 = Train A’s time, and d1 = Train A’s distance traveled.

Similarly, we will let r2 = Train B’s rate, t2 = Train B’s time, and d2 = Train B’s distance traveled.

The individual distance traveled by Train A will be:

r1 x t1 = d1 (Equation 1)

The individual distance traveled by Train B will be:

r2 x t2 = d2 (Equation 2)

Because the distance between the two cities is 311 miles, we can say that: the sum of the individual distances is equal to the total distance:

d1 + d2 = 311

We can substitute Equation 1 and Equation 2 into Equation 3, as follows:

r1 x t1 + r2 x t2 = 311

Substituting the known information for the rates of the two trains, we have:

50 x t1 + 60 x t2 = 311 (Equation 4)

We have two variables and only one equation, so we need additional information about the relationship between the two times. Because Train B left half an hour after Train A, its travel time is half an hour less than Train A’s. Thus, we see that t2 = t1 – 0.5, and we substitute this into Equation 4 and solve:

50 x t1 + 60 x (t1 – 0.5) = 311

50 x t1 + 60 x t1 – 30 = 311

110 x t1 = 341

Since Train A traveled for 3.1 hours, we substitute this value into Equation 1:

50 x 3.1 = d1

Train A traveled 155 miles.

Next, let’s discuss how to find the median of a large set of data.

GMAT Problem Solving Topic 4: Statistics – Finding the Median of a Large Set of Data

If you have ever studied how to determine the median of a set of data, you may recall that it’s a pretty simple process when you have a small set of data, as you can manually calculate it pretty easily. However, what do you do when you have a large set of data? Don’t worry; there’s an excellent way to determine the median, even in a large set!

To determine the place where the median falls in a set of data in ascending or descending order, we use the following formula, where n represents the total number of values in the set:

position of the median = (n + 1) / 2

Keep in mind that this formula works when the number of data points is odd and when it’s even, but in slightly different ways. Let’s do two quick examples that illustrate the difference.

Median Example With an Odd Number of Numbers

What is the median of -4, -3, 0, 1, 4, 6, 10, 11, 15?

Since there are nine numbers in the ordered set, we can determine the position of the median as follows:

position of the median = (9 + 1) / 2 = 5

So, the median is the 5th number in the set when counting from lowest to highest. Thus, the median is 4. Now let’s look at a set with an even number of numbers.

Median Example With an Even Number of Numbers

What is the median of -4, -3, 0, 1, 2, 6, 10, 11, 15, 19?

Since there are ten numbers in the set, we can determine the position of the median as follows:

position of the median = (10 + 1) / 2 = 5.5

Since the median cannot be in the “5.5 position” of the set, we calculate the average of the number in the fifth and sixth positions. The number in the fifth position is 2, and the number in the sixth position is 6. The average of those two numbers is 8/2 = 4. So, the median is 4.

The position of the median of an ordered data set is found by using the formula: position of median = (n + 1) / 2, where n is the number of values in the set.

GMAT Problem Solving Example 4:

At a candy shop, there are sixteen candies costing $1 each, twenty candies costing $2 each, and forty candies costing $3 each. What is the median cost of the candies?

Let’s calculate the position of the median for the 76 candies:

Position of median = (n + 1) / 2 = (76 + 1) / 2 = 77 / 2 = 38.5

We know that the median is the average of the 38th and 39th data values.

We don’t have the 77 data values listed individually, but we know that we are looking for the 38th and 39th data values. We see that the first 16 values are all $1, and the next 20 values (the 17th through 36th values) are all $2. The next 20 values (the 37th through the 66th values) are all $3.

Thus, we see that both the 38th and the 39th data values are each $3. Thus, the median is $3.

Next, let’s discuss one final GMAT Problem Solving topic: three-part ratios.

GMAT Problem Solving Topic 5: Ratios – Three-Part Ratios

Three-part ratios are one of the more challenging topics tested in ratios. Three-part ratio problems generally present two two-part ratios with a shared term represented by different numbers in each ratio.

For example, we may be given the following two ratios concerning the number of cartons of white milk, chocolate milk, and strawberry milk in a New York deli.

White to Chocolate = 3 to 2

White to Strawberry = 5 to 4

In the first ratio, the number of cartons of white milk is represented by 3. In the second ratio, the number of cartons of white milk is represented by 5. However, we need the number of cartons of white milk to be represented by the same number in both ratios before we can combine the two ratios into a single three-part ratio.

The LCM of 3 and 5 is 15. Thus, we’ll be able to combine the ratios if we create two equivalent ratios such that both have the number of cartons of white milk represented by 15:

White to Chocolate = 3 to 2 = 3 × 5 to 2 × 5 = 15 to 10

White to Strawberry = 5 to 4 = 5 × 3 to 4 × 3 = 15 to 12

Now that both equivalent ratios have the same number, 15, representing the number of cartons of white milk, we can create the following three-part ratio:

White : Chocolate : Strawberry = 15 : 10 : 12

To convert two two-part ratios to one three-part ratio, use the LCM of the common item shared by both ratios.

Let’s now try a Problem Solving example dealing with this concept.

At a farm, the ratio of horses to ponies is 10 : 7, and the ratio of goats to ponies is 3 : 2. If there are 60 horses at the farm, how many goats are there?

The common connection in the two ratios is ponies, so we need to find the LCM of the two “ponies” numbers, which are 7 and 2. Thus, the LCM is 7 x 2 = 14.

We can now convert the first ratio of horses to ponies, 10 : 7, to one in which the number of ponies in the ratio is 14, by multiplying by 2:

Horses to ponies = 10 to 7 = (10 x 2) to (7 x 2) = 20 to 14

Similarly, to convert the goats : ponies ratio, currently 3 : 2, such that the number of ponies in the ratio is 14, we multiply the ratio by 7.

Goats to ponies = 3 : 2 = (3 x 7) to (2 x 7) = 21 to 14

The three-part ratio can now be stated as horses : ponies : goats = 20 : 14 : 21.

There are 60 horses at the farm. If we multiply the three-part ratio by 3, we obtain the equivalent ratio of horses : ponies : goats as 60 : 42 : 63. Thus, there are 63 goats at the farm.

Whether you are registered for the GMAT or the GMAT Focus Edition, Problem Solving questions will constitute a large part of the quantitative portion of your exam. The more exposure you have to the various topics tested by PS questions, the better prepared you’ll be on test day.

In this article, we have focused on 5 examples of PS questions you might encounter on the GMAT or the GMAT Focus. They have come from the major topics of Number Properties, Inequalities, Rates, Statistics, and Ratios. They represent only a small proportion of the topics and subtopics that you need to master in order to get a great score on the GMAT.

The PS questions we covered in this article represent only a small proportion of the topics and subtopics that you need to master in order to get a great score on the GMAT. Check out our article that introduces additional GMAT PS math questions for more practice and expert tips!

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Jeffrey Miller is the head GMAT instructor for Target Test Prep. Jeff has more than fourteen years of experience in the business of helping students with low GMAT scores hurdle the seemingly impossible and achieve the scores they need to get into the top 20 business school programs in the world, including HBS, Stanford, Wharton, and Columbia. Jeff has cultivated many successful business school graduates through his GMAT instruction, and will be a pivotal resource for many more to follow.

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7 Tips To Master GMAT Focus Quantitative Section for a Stellar Score

Mar 22, 2023 | GMAT

Understanding the GMAT Focus Quantitative Landscape

The Quantitative Reasoning section within the GMAT Focus Edition serves as a pivotal assessment of an individual’s foundational arithmetic and elementary algebraic proficiency, emphasizing the application of these skills to navigate intricate problem-solving scenarios. With a condensed format comprising 21 Problem-Solving questions, this section is time-bound, spanning 45 minutes. Notably, the removal of Data Sufficiency questions to the Data Insights Section and the exclusion of geometry queries mark a distinct shift in this edition’s focus. Moreover, the continued prohibition of calculators underscores the test’s emphasis on mental math and strategic problem-solving approaches.

Problem-solving questions , multiple-choice in nature, evaluate logical and analytical prowess. Crucially, these question types revolve around algebra and arithmetic. There’s no need to fret about trigonometry or calculus; basic high school-level math serves as the foundation for the GMAT Quantitative Section.

Decoding the Difficulty of GMAT Quantitative Section

Despite the apparent simplicity of math concepts, the GMAT Quantitative Section poses challenges through time constraints and the absence of calculators.

Here are seven tips tailored to navigate through these challenges and elevate your quant section performance:

• Understand the Evolving Format: With 21 math problems to solve in 45 minutes, averaging around two minutes per question, grasp the nuances of the GMAT Focus Edition Quantitative Section. While time management is crucial, allocate additional time to intricate problems when needed, adapting to the new test format.
• Don’t overthink the math: First and foremost, don’t forget that the GMAT Focus quant section consists of simple math problems. Use this to your advantage. Don’t do all of the calculations; rather, determine what makes a problem look more difficult than it actually is.
• Start managing your time before the test: You can start saving time before you even pick up your pencil by practicing arithmetic. Limiting the time it takes to do simple equations means you can spend more time on the problems. Be sure to review exponent rules and brush up on decimals with fractions. And don’t forget about higher powers!
• Use alternative strategies to find solutions: If you can’t solve a problem with simple math, try using an alternative path to the solution. There’s usually an easier way to solve quant problems–the GMAT is designed to test for efficient problem solving. Sometimes, straightforward logic or plugging in numbers will solve a problem faster. Keep in mind that a traditional approach might not be necessary for every problem.
• Analyze each sentence step by step: During the GMAT preparation process, learn how to simplify each question. Some problems might seem daunting, but they can be broken into smaller steps that you can solve one-by-one. Trying to solve the whole problem at once can lead test takers to answer the wrong question. The more you break down the problem, the easier it will become. Don’t worry–you’ll actually save time by (re-)reading the questions.
• Scratch paper is a must: Although scratch paper may seem unnecessary for quant problems, it can help you keep track of calculations and clarify your thought process. It might take a little extra time, but ultimately, avoidable mistakes are even more time consuming.
• Plug in the answer choices: Another way to save time with alternative solution paths is to start by reading all of the answer choices and plugging them into the problem. If you don’t know which answer choices to start with, start from the middle.

Bonus Tip: Diversify Your Preparation: Integrate diverse preparation methods, including rule memorization, video tutorials, and updated professional courses tailored for the GMAT Focus Edition, ensuring a comprehensive skill set.

Embark on your GMAT journey equipped with these strategies, and you’ll forge a path toward conquering the Quantitative Section. Stay tuned for more insights into GMAT preparation. Best of luck on your exam!

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• A Guide to Combinatorics on the GMAT
• Ordering in Combinatorics: A Guide to Solving GMAT Questions
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• Admissions (14)
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• GMAT Quantitative Reasoning: A Comprehensive Guide

Table of Contents

Importance of quantitative reasoning section in the gmat exam , understanding gmat quantitative reasoning, common challenges faced by test-takers, key strategies for problem solving questions, strategies for data sufficiency questions , practice resources for gmat quantitative reasoning section, tips to improve quantitative reasoning skills.

Are you ready to conquer the quantitative reasoning section of the GMAT? The GMAT Quantitative Reasoning section can be a daunting challenge for many test-takers. From complex algebraic equations to intricate data analysis, this part of the exam requires a sharp analytical mind and solid mathematical skills. However, fear not! With the right approach and preparation, you can tackle this section with confidence and ace the GMAT.

In this comprehensive guide, we'll dive deep into the GMAT Quantitative Reasoning section, offering insights, strategies, and tips to help you navigate through the questions successfully. Whether you're a math whiz or someone who dreads numbers, this guide is your key to unlocking the secrets of GMAT Quantitative Reasoning.

The Quantitative Reasoning section of the GMAT plays a crucial role in assessing a candidate's ability to analyze and solve quantitative problems. This section is designed to evaluate your proficiency in basic mathematical concepts and your ability to reason quantitatively. It goes beyond testing mere calculation skills, focusing more on your understanding of mathematical principles and your ability to apply them to real-world scenarios. Strong performance in this section not only demonstrates your quantitative abilities but also showcases your analytical thinking and problem-solving skills, which are highly valued in the business world.

Following are the key reasons why the Quantitative Reasoning section is important:

• Business School Readiness: Business schools use the GMAT as a benchmark to assess candidates' readiness for their programs. The Quantitative Reasoning section helps admissions committees evaluate whether applicants possess the quantitative skills necessary for success in graduate-level business courses.
• Problem-Solving Skills: The section goes beyond testing mathematical knowledge; it assesses your ability to apply quantitative reasoning to solve real-world problems. This skill is essential for business professionals who need to make data-driven decisions.
• Competitive Edge: A strong performance in the Quantitative Reasoning section can give you a competitive edge in the admissions process. It demonstrates to schools that you have the quantitative skills necessary to excel in their programs.
• Career Opportunities: Mastering quantitative reasoning can open up various career opportunities in fields such as finance, consulting, and marketing, where data analysis and problem-solving skills are highly valued.
• Overall GMAT Score: The Quantitative Reasoning section contributes to your overall GMAT score, which is a critical factor in the admissions process. A high score in this section can offset weaknesses in other areas and improve your overall competitiveness as an applicant.

Below is a table summarizing the importance of the Quantitative Reasoning section in the GMAT exam:

The Quantitative Reasoning section is a fundamental part of the GMAT exam that evaluates your quantitative skills, problem-solving abilities, and readiness for graduate-level business education. Achieving a strong score in this section can significantly enhance your candidacy for admission to top business schools and pave the way for a successful career in the business world.

Navigating the GMAT Quantitative Reasoning section requires a solid understanding of its components and objectives. This section evaluates your ability to solve quantitative problems and interpret data accurately. By mastering the two question types: Problem Solving and Data Sufficiency and honing essential skills, you can approach this section with confidence.

However, it's essential to be aware of common challenges that test-takers encounter, such as time management issues and difficulty in deciphering complex problem scenarios. Let's delve deeper into the breakdown of question types, the skills assessed, and the hurdles you may face during your GMAT preparation journey. 

Exploring the Question Types: Problem Solving and Data Sufficiency

The GMAT Quantitative Reasoning section comprises two main question types: Problem Solving and Data Sufficiency. Each type assesses your quantitative reasoning abilities in unique ways.

1. Problem Solving

In the Problem Solving questions, you are presented with a mathematical problem and five answer choices. Your task is to determine the correct answer based on the information provided. These questions require you to apply mathematical concepts and reasoning skills to solve problems efficiently.

2. Data Sufficiency

Data Sufficiency questions are designed to test your ability to analyze a problem, determine what information is needed to solve it, and assess whether the given information is sufficient to reach a solution. You are presented with a question and two statements, and you must decide whether each statement alone or both statements together are sufficient to answer the question.

Following table provides a concise overview of the key differences between the two question types:

Skills and Knowledge Assessed in GMAT Quantitative Reasoning Section

The GMAT Quantitative Reasoning section assesses a range of skills and knowledge areas that are crucial for success in graduate-level business programs and beyond. Here are some key skills and knowledge areas assessed in this section:

• Mathematical Proficiency: A solid foundation in basic mathematical concepts such as algebra, geometry, and arithmetic is essential. You should be comfortable with calculations, equations, and mathematical relationships.
• Problem-Solving Abilities: The ability to analyze and solve complex quantitative problems is paramount. You should be able to understand problem scenarios, identify relevant information, and apply appropriate problem-solving strategies.
• Data Interpretation: This section often includes questions that require you to interpret data presented in various formats, such as tables, charts, and graphs. You should be able to extract relevant information and draw conclusions based on the data provided.
• Logical Reasoning: Many questions in this section require logical reasoning skills. You should be able to follow logical arguments, identify patterns, and make logical deductions.
• Quantitative Comparison: In Data Sufficiency questions, you need to compare quantities and determine their relationship. This requires a strong understanding of numerical relationships and the ability to make logical comparisons.
• Critical Thinking: The ability to think critically and evaluate the validity of arguments is important. You should be able to assess the soundness of mathematical reasoning and identify flaws in arguments.

By developing these skills and knowledge areas, you can improve your performance in the GMAT Quantitative Reasoning section and enhance your overall GMAT score.

Preparing for the GMAT Quantitative Reasoning section comes with its own set of challenges. Being aware of these challenges can help you develop strategies to overcome them effectively. Here are some common challenges faced by test-takers:

• Time Constraints: The GMAT Quantitative Reasoning section is timed, and you have to answer a series of questions within a limited time frame. Managing your time effectively and avoiding spending too much time on any single question can be challenging.
• Complex Problem Scenarios: Some questions present complex problem scenarios that require careful reading and understanding. It can be challenging to decipher the information provided and determine the correct approach to solving the problem.
• Data Interpretation: Questions that involve interpreting data presented in tables, charts, and graphs can be challenging. You need to extract relevant information and make accurate interpretations to answer the questions correctly.
• Quantitative Comparison: Data Sufficiency questions, which require you to compare quantities and determine their relationship, can be tricky. Understanding the requirements of each question and avoiding common traps can be challenging.
• Mathematical Concepts: The GMAT Quantitative Reasoning section tests your knowledge of basic mathematical concepts such as algebra, geometry, and arithmetic. It can be challenging if you are not familiar with these concepts or if you have not practiced them recently.
• Logical Reasoning: Some questions require logical reasoning skills to identify patterns, make deductions, and evaluate arguments. Developing these skills can be challenging, especially if you are not accustomed to thinking in a logical and analytical manner.

By recognizing these common challenges and preparing accordingly, you can improve your chances of success in the GMAT Quantitative Reasoning section. Practice regularly, familiarize yourself with the question types, and develop effective strategies for time management and problem-solving.

Mastering Problem Solving questions in the GMAT Quantitative Reasoning section demands not only mathematical proficiency but also strategic thinking. These questions are designed to test your ability to apply mathematical concepts to real-world scenarios. To excel, you must approach each question methodically, employing various strategies to optimize your performance. Here are some effective strategies to tackle Problem Solving questions.

1. Approaching Different Question Types

Problem Solving questions in the GMAT Quantitative Reasoning section encompass various mathematical concepts, including algebra, arithmetic, and geometry. Each question type requires a unique approach to solve efficiently. Here's how you can approach different question types:

• Algebra: Translate word problems into algebraic equations or expressions. Look for patterns and relationships between variables to solve the problem efficiently.
• Arithmetic: Focus on simplifying calculations and avoiding unnecessary steps. Look for shortcuts or alternative methods to solve arithmetic problems quickly and accurately.
• Geometry: Visualize geometric figures and relationships to solve geometry problems. Break down complex shapes into simpler components and apply relevant geometric formulas or principles.

Here's a concise approach for each question type, presented in a table:

2. Time Management Tips

Effective time management is crucial for success in the GMAT Quantitative Reasoning section. Here are some time management tips to help you tackle Problem Solving questions:

• Prioritize Questions: Start with questions that you find easier and can solve quickly. Skip challenging questions initially and come back to them later if time permits.
• Set Time Limits: Allocate a specific amount of time to each question and stick to it. If you're spending too much time on a single question, move on to the next one and come back later if time allows.
• Flag Questions: Use the flagging feature to mark questions that you find particularly challenging or time-consuming. This allows you to easily identify and revisit these questions later.

3. Using the Answer Choices to Your Advantage

The answer choices in Problem Solving questions can provide valuable clues to help you arrive at the correct answer. Here are some strategies for using the answer choices to your advantage:

• Plug-In Method: Substitute answer choices into the problem to see which one satisfies the given conditions. This can help you eliminate incorrect choices and narrow down the correct answer.
• Backsolving: Start with the answer choices and work backward to see which one fits the problem conditions. This can be particularly effective for algebraic or numerical problems.
• Estimation: If exact calculations are time-consuming, use estimation to quickly narrow down the answer choices. Eliminate choices that are significantly higher or lower than your estimated value.

By employing these strategies, you can approach Problem Solving questions with confidence, efficiently manage your time, and increase your chances of selecting the correct answer. Practice applying these strategies to a variety of question types to become more proficient and comfortable with Problem Solving questions on the GMAT.

Data Sufficiency questions in the GMAT Quantitative Reasoning section are unique in their approach, testing not just your mathematical prowess but also your analytical skills. These questions present a scenario followed by two statements, challenging you to discern whether the given data is adequate to solve the problem. Crafting a successful strategy involves mastering the art of discerning sufficiency, often through process of elimination and identifying the minimum information needed for a conclusive answer. Here, we delve into strategies to tackle Data Sufficiency questions adeptly, maximizing your performance on the GMAT. 

1. Format of Data Sufficiency Questions

Data Sufficiency questions consist of a question followed by two statements labeled (1) and (2). Your task is not to solve the problem but to determine whether the information provided in the statements is sufficient to answer the question.

Here's how to approach the format of Data Sufficiency questions:

• Identify the Question: Understand what the question is asking and what type of information is needed to answer it.
• Analyze the Statements: Evaluate each statement independently to determine whether it provides enough information to answer the question. Remember, you don't need to solve the problem; you just need to assess sufficiency.
• Consider Both Statements Together: If neither statement alone is sufficient, assess whether combining both statements provides enough information to answer the question.

2. Process of Elimination

Use the process of elimination to systematically eliminate answer choices and narrow down the correct answer. Here's how to use this strategy effectively:

• Eliminate Obviously Insufficient Statements: If a statement clearly does not provide enough information to answer the question, eliminate it as a possible answer.
• Focus on Unique Information: Look for unique or specific information in each statement that could potentially provide a definitive answer to the question.
• Consider Extreme Cases: Test extreme cases or hypothetical scenarios to determine whether the statements provide consistent or contradictory information.

3. Identifying the Minimum Information Required to Answer the Question

In Data Sufficiency questions, you don't need to solve the problem completely; you just need to determine whether the information provided is sufficient to arrive at a single, definite answer. Here's how to identify the minimum information required:

• Focus on the Question Stem: Understand exactly what the question is asking for and what type of information is needed to answer it.
• Identify Redundant Information: Avoid getting distracted by extraneous or redundant information provided in the statements. Focus on identifying the essential information required to answer the question.
• Assess Combined Sufficiency: If neither statement alone is sufficient, assess whether combining both statements provides enough information to answer the question definitively.

By employing these strategies, you can approach Data Sufficiency questions with confidence, efficiently analyze the information provided, and increase your chances of selecting the correct answer. Practice applying these strategies to various question types to become more proficient and comfortable with Data Sufficiency questions on the GMAT.

To excel in the GMAT Quantitative Reasoning section, it's crucial to practice with high-quality study materials and practice questions. Here are some recommended resources to enhance your preparation:

Recommended Study Materials and Practice Questions

Strengthening your skills for the GMAT Quantitative Reasoning section requires effective practice with reliable study materials and practice questions. Here's how to make the most of your practice resources:

• Official GMAT Prep Materials: Utilize the official GMAT study materials, including the Official Guide for GMAT Review, to familiarize yourself with the question types and format of the exam.
• Online Practice Platforms: Explore online platforms such as GMAT Club and Manhattan Prep for additional practice questions and resources tailored to GMAT preparation.
• Quantitative Reasoning Workbooks: Work through specialized workbooks focusing on quantitative reasoning to strengthen your problem-solving skills.
• GMAT Prep Courses: Consider enrolling in GMAT prep courses offered by reputable test prep companies, which often include access to practice questions and simulated exams.
• Private Tutoring: If needed, seek private tutoring to receive personalized guidance and targeted practice to address specific areas of weakness.

Importance of Mock Tests and How to Use Them Effectively

Mock tests are a critical component of GMAT preparation, providing a simulated test-taking experience that helps you gauge your readiness and identify areas for improvement. Here's how to make the most of mock tests:

• Regular Practice: Take mock tests regularly to build stamina and familiarity with the exam format.
• Review Mistakes: After taking a GMAT mock test , thoroughly review your answers to understand the reasoning behind correct and incorrect choices.
• Time Management Practice: Use mock tests to practice effective time management strategies and simulate real exam conditions.
• Identify Weaknesses: Pay attention to the types of questions or topics where you struggle, and focus your study efforts on improving in these areas.
• Track Progress: Keep track of your mock test scores over time to monitor your progress and adjust your study plan accordingly.

By utilizing these practice resources and incorporating mock tests into your study routine, you can strengthen your quantitative reasoning skills and improve your performance on the GMAT exam.

Developing strong quantitative reasoning skills is essential for success in the GMAT Quantitative Reasoning section. Here are some tips to enhance your skills and excel in this section:

• Practice Regularly: Dedicate time each day to practice quantitative problems. Start with basic concepts and gradually move to more complex problems to build your skills.
• Understand Fundamentals: Ensure you have a solid understanding of fundamental mathematical concepts such as algebra, geometry, and arithmetic. Strengthening these basics will help you tackle more advanced problems with ease.
• Solve a Variety of Problems: Work on problems from different areas of mathematics to develop a versatile skill set. This will also help you become familiar with the different question types on the GMAT.
• Focus on Problem Solving Techniques: Learn and practice various problem-solving techniques, such as algebraic manipulation, geometric visualization, and numerical estimation. These techniques can help you solve problems more efficiently.
• Review Mistakes: When you make a mistake, take the time to understand why it happened. Identify any gaps in your understanding and work on improving those areas.

By following these tips and consistently practicing, you can strengthen your quantitative reasoning skills and boost your confidence for the GMAT Quantitative Reasoning section.

In conclusion, mastering the GMAT Quantitative Reasoning section requires a strategic approach and diligent practice. Understanding the question types, developing problem-solving techniques, and managing time effectively are key. Utilizing recommended study materials, taking mock tests, and seeking feedback are essential strategies for improvement. Success on the GMAT demands not just knowledge but also skillful application. With dedication and perseverance, you can strengthen your quantitative reasoning skills and achieve your target score. 

Frequently Asked Questions (FAQs)

What is the best way to prepare for the GMAT Quantitative Reasoning section?

The best way to prepare is to practice regularly with a variety of quantitative problems. Familiarize yourself with the question types and formats, and use official GMAT study materials for practice.

How important is time management in the GMAT Quantitative Reasoning section?

Time management is crucial, as you have a limited amount of time to answer a series of questions. Practice pacing yourself and prioritize questions to maximize your score.

Are there any specific tips for improving performance in Data Sufficiency questions?

Focus on understanding the question stem, analyzing each statement independently, and considering both statements together if necessary. Use the process o.f elimination and identify the minimum information required to answer the question

What role do mock tests play in GMAT Quantitative Reasoning preparation?

Mock tests are essential for simulating the real exam experience and assessing your readiness. They help you identify strengths and weaknesses, refine your test-taking strategies, and build confidence for the actual exam.

How can I improve my quantitative reasoning skills if I struggle with certain concepts?

If you find certain concepts challenging, seek additional help from tutors, study groups, or online resources. Focus on understanding the fundamentals and practice consistently to build your skills over time.

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Miscellaneous GMAT-Specific Strategies

Shortest path graphic 2.png.

Note: This is article #3 in the multi-article series Are you doing it wrong?

In my previous article , we examined the strategy of testing the answer choices, which is just one of the ways to exploit the fact that the correct response to every GMAT Problem Solving question is hiding among the five answer choices. 

In this article, we’ll examine 5 more ways to use the answer choices to our advantage: 

• Testing solutions to given equations and inequalities
• Testing for equivalency
• Testing values that satisfy the given conditions 
• Geometry by visual estimation
• Gut-driven probabilities

1. Testing solutions to given equations and inequalities

The GMAT asks a lot of What Must Be True questions. These questions present us with some mathematical truth in the form of an equation or inequality, and we must determine which statement among the answer choices must also be true. Here’s an example from the GMAT Official Guide : 

If y + |y| = 0 which of the following must be true?

(A) y > 0

(C) y < 0

On GMAT Club, 35% of students get this question wrong. Most students will try to apply (with varying success) one or more mathematical properties to solve this question, whereas the faster (and more accurate) approach is to use the answer choices to our advantage. 

If y + |y| = 0, we can easily see that it could be the case that y = 0 . 

Now we’ll plug y = 0 into the five answer choices to see which one(s) is/are true: 

A. 0 > 0. Not true. Eliminate. 

B. 0 ≥ 0. True. Keep.

C. 0 < 0. Not true. Eliminate.

D. 0 ≤ 0. True. Keep.

E. 0 = 0. True. Keep.

We’re already down to options B, D and E. 

Aside: When looking for solutions to a given equation or inequality, it's useful to first check whether 0 is a solution, since zero is such an easy value to work with.

Now we’ll test another y-value that satisfies the equation y + |y| = 0

We can see that y = -1 is another possible solution. So, we’ll plug y = -1 into the remaining three answer choices: 

B. -1 ≥ 0. Not true. Eliminate.

D. -1 ≤ 0. True. Keep.

E. -1 = 0. Not true. Eliminate.

By the process of elimination, the correct answer is D.

This efficient strategy also works with 700+ level inequality questions like this one from the GMAT Club tests: 

If (|x| - 2)(x + 5) < 0, then which of the following must be true?

(A) x > 2

(B) x < 2

(C) -2 < x < 2

(D) -5 < x < 2

(E) x < -5

On GMAT Club, this question has a success rate of 28%.  

Let’s first find an x-value that satisfies the given inequality (|x| - 2)(x + 5) < 0. 

It turns out x = 0 is a solution. Now plug x = 0 into the five answer choices: 

(A) 0 > 2. Not true. Eliminate. 

(B) 0 < 2. True. KEEP. 

(C) -2 < 0 < 2. True. KEEP.

(D) -5 < 0 < 2. True. KEEP.

(E) 0 < -5. Not true. Eliminate.

We’re now down to choices B, C and D. 

Now let’s find an “extreme” x-value that satisfies (|x| - 2)(x + 5) < 0. 

x = -10 works. So, we’ll plug x = -10 into the remaining three answer choices:

(B) -10 < 2. True. KEEP. 

(C) -2 < -10 < 2. Not true. Eliminate.

(D) -5 < -10 < 2. Not true. Eliminate.

By the process of elimination, the correct answer is B.

Here are a few more questions to practice with: 

Sub 600 Level

• Question 1 | my solution
• Question 2 | my solution
• Question 3 | my solution

2 - Testing for Equivalency

This next strategy can be applied to questions in which we’re given some algebraic expression, and we must identify an equivalent expression among the answer choices. 

The GMAT-specific strategy for this question type relies on the following property: 

If two algebraic expressions are equivalent, they must evaluate to the same value for every possible value of x. 

For example, since the expression 2x + 3x is equivalent to the expression 5x, the two expressions will evaluate to the same number for every value of x. So, for example, when x = 7, the expression 2x + 3x = 2(7) + 3(7) = 14 + 21 = 35 ; likewise, the expression 5x = 5(7) = 35 .

Let’s apply this strategy to the following question from the GMAT Official Guide : 

If k and n are positive integers such that n > k, then k! + (n - k)(k -1)! is equivalent to which of the following?

(A) (k)(n!)

(B) (k!)(n)

(C) (n - k)!

(D) (n)(k + 1)!

(E) (n)(k - 1)!

Since we’re told k and n are positive integers such that n > k, let’s first see what the given expression evaluates to when n = 3 and k = 2.

When we plug these values into the given expression, we get: k! + (n - k)(k -1)! = 2! + (3 - 2)(2 -1)! = 2! + (1)(1!) = 2 + 1 = 3. 

So, when n = 3 and k = 2, the given expression evaluates to 3. This means the correct answer must also evaluate to 3 , when n = 3 and k = 2

To find out, we'll plug n = 3 and k = 2 into the five answer choices:

(A) (k)(n!) = (2)(3!) = (2)(6) = 12 . Eliminate.

(B) (k!)(n) = (2!)(3) = (2)(3) = 6 . Eliminate.

(C) (n - k)! = (3 - 2)! = 1! = 1 . Eliminate.

(D) (n)(k + 1)! = (3)(2 + 1)! = (3)(3!) = (3)(6) = 18 . Eliminate.

(E) (n)(k - 1)! = (3)(2 - 1)! = (3)(1!) = (3)(1) = 3 . Perfect!!

If more than one answer choice evaluated to 3 for n = 3 and k = 2, then we’d have to test another pair of values on the remaining answer choices. 

Here are a few practice questions:

3 - Testing values that satisfy the given conditions

Another GMAT-specific strategy is testing values that adhere to the conditions provided in the question. This strategy works especially well with Integer Properties questions such as this one from the Official Guide :

If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?

(B)     Three

(C)     Four

(D)     Six

(E)     Eight

On GMAT Club, this question has a 700+ rating. Having reviewed it with dozens (perhaps hundreds) of students, I know that many try to apply logic that goes something like this: 

If p is a prime greater than 2, then p is odd. If p is odd, then 2p is even and, since 2p is a divisor of 4p, we know that 2p must be an even divisor of 4p. Similarly, 4p will be another even divisor of 4p, . . . etc. 

This approach (although admirable) pales in comparison to simply testing a value of n that satisfies the given information. 

Since p is a prime number greater than 2, it could be the case that p = 3.

Substitute into given equation to get: n = 4p = 4(3) = 12

If n = 12 , the positive divisors of n are 1, 2, 3, 4, 6 and 12. Among these divisors, four are even (2, 4, 6, and 12), which means the correct answer is C.  

Here’s another official GMAT question: 

At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

Since each night crew worker loaded 3/4 as many boxes as each day crew worker, it could be the case that each day crew worker loaded 4 boxes, and each night crew worker loaded 3 boxes.  

Since the number of night crew workers is 4/5 the number of day crew workers, it could be the case that there are 5 day crew workers, and 4 night crew workers. 

If there are 5 day crew workers, and each day crew worker loaded 4 boxes, then the day crew loaded a total of 20 boxes. 

Similarly, if there are 4 night crew workers, and each night crew worker loaded 3 boxes, then the night crew loaded a total of 12 boxes. 

20 + 12 = 32 , which means the two crews loaded a total of 32 boxes. 

Since the day crew loaded 20 boxes, the required fraction = 20/32 = 5/8

Here are some questions to practice the above strategy:

4 - Geometry by visual estimation

Another area where we can use the answer choices to our advantage involves an important feature regarding the geometric figures accompanying GMAT Problem Solving questions. 

Consider this question from the Official Guide : 

Geometry-visual-estimation-Q.png

The key ingredient of this strategy is the fact that the geometric diagrams in GMAT Problem Solving questions are drawn to scale unless stated otherwise . So, in some cases, we may be able to identify the correct answer through visual approximation alone.  

Here, the question tells us the diameter = 2, which means PO (the radius) has length 1. 

When we compare the lengths of PO and RT, we see that RT is slightly longer, which means RT is slightly longer than 1. 

Now let’s evaluate each answer choice by replacing √3 with its approximate value of 1.7 

Tip: Before test day, be sure to memorize the following approximations: √2 ≈ 1.4, √3 ≈ 1.7, and √5 ≈ 2.2. These values come in handy A LOT.  

When we replace √3 with 1.7, we get: 

A) 1/2 = 0.5

B) 1/1.7 = a number that’s less than 1. 

C) 1.7/2 = a number that’s less than 1.

D) 2/1.7 = a number that’s a little bit bigger than 1. 

E) 1.7 = a number that’s 70% bigger than 1.

We can see that answer choice D is the only one that suits our approximation. 

The test-makers know that some students will bypass geometric reasoning altogether and attempt to answer the question by estimating the length of RT. Given this, you’d think they’d have more than just one answer choice that’s slightly greater than 1, but they didn’t. Another gift from our benevolent test-makers! 

Here’s another official question where we can easily identify the correct answer solely through visual approximation (my solution here ). 

Can all GMAT geometry questions be solved by visual approximation? 

Absolutely not. In fact, most can’t be solved this way. That said, there are many questions where we can visually estimate the answer and then eliminate 2 or 3 options, which makes for an expedient guess if you’re behind time, or you have no idea how to solve the question. 

It’s also worth noting that, even if we solve a geometry question via conventional strategies, we can still use visual approximation to confirm our solution. 

For example, in this question from the Official Guide , we must determine what fraction of the larger circle is shaded. If your calculations yielded an answer of 1/2 (answer choice E), a quick visual inspection of the given diagram would be enough to tell you your calculations were incorrect.  

Here are a few more examples to try: 

5 - Gut-driven probabilities

This last strategy relies on our innate ability to estimate the likelihood of an event. For example, even if we know nothing about probability rules, we still have a “gut feeling” about the probability of randomly selecting 2 queens from a deck of playing cards in two draws. We certainly know the probability is less than 1/5, which means we can eliminate any answer choices greater than 1/5. This isn’t to say you’ll be able to eliminate 4 answer choices, but in many cases, you’ll be able to eliminate some answer choices, which is better than a 1-in-5 guess.    

For example, consider this official GMAT question: 

A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?

Check out the extremes. Do you think the two middle rosebushes will be red half the time? Seems unlikely, so we can eliminate E. What about 1/12? And so on. 

Here’s my full solution to that question. 

Test out your gut feeling “skills” with these questions:

Final Words 

As you can see, the test-makers often provide opportunities to use time-saving (and error-reducing strategies). Always remember that the every GMAT quantitative question is testing your ability to identify the correct answer in the most efficient manner. Sometimes, conventional strategies are more efficient, and sometimes GMAT-specific strategies are. 

So, as you practice with official questions, practice identifying the most efficient approach. Afterwards, you can try answering the question via the other approach.

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GMAT Strategies – Non-Traditional Math Techniques

Gmat problem solving – gmat strategies.

The good news is that there is a better way on the GMAT. The traditional way of approaching many GMAT problem solving questions is often the least effective and least efficient way to get a right answer, which of course is your ultimate goal. Why set up an algebraic equation and solve for “x” when you can use the answer choices to your advantage, for example? Your goal should be to get easy and difficult GMAT problem solving questions correct with as little effort in as little time as possible — and this course will help you to do just that.

It may just be the most important and impactful lesson you learn in your preparation for the GMAT, so prepare to shift your thinking and boost your GMAT math score immediately.

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• Detailed introduction to GMAT problem solving;
• Discussion of the ideal mental approach for attacking GMAT problem solving questions;
• How to make questions involving variables more concrete and easier to solve;
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• How to use they answer choices to your advantage to save time and ultimately get more right answers;
• The “WIBNI” master GMAT math move;
• How to approximate right answers when you feel stuck or don’t know how to solve a question exactly;
• Strategic guessing and elimination strategies;
• How figures work on GMAT problem solving questions, and how to use those figures to your advantage to get right answers even when you’re unsure of the traditional geometric approach;

The course also includes a 20-question practice assessment , available as an online quiz or downloadable PDF worksheet, enabling you to apply what you’re learning in the course to real sample GMAT problem solving questions. There are detailed video solutions for each of the questions to ensure that you’re applying the correct strategy and truly mastering the concepts.

So what are you waiting for? Take your GMAT preparation to the next level. Add this course to your library now and prepare to dominate the GMAT!

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GMAT Problem Solving Strategies

Strategies for problem solving in GMAT are very useful during the preparation process. It will help a GMAT applicant in understanding the fundamental concepts and utilizing it to solve the quantitative problems. GMAT strategies for problem solving trains an individual on how to apply their mathematical understanding, accompanied by logical reasoning, rather than just finding the accurate answers. The strategies for problem solving are explained below.

Strategies for Problem Solving

• Strong Fundamentals

Work on the simple problems as a first task because it does not require too much of time. The most important aspect of problem solving section is you should be strong in basic mathematical calculations. There are common things which should be familiarized viz. powers, roots, multiplying and dividing decimals. These form the basics for certain mathematical calculations and added to this fact, no calculators are allowed in a test center. When you are familiar with these basic things it will not take much time for you to complete the plain mathematical calculations.

• Pencil and Scratch Paper

Always use a pencil and scratch papers for rough calculations. This would help you to prevent making errors in multiple choice questions because once the answer is given in a test, it cannot be changed. So work on a scratch paper and then answer the questions.

• Shortcuts and Techniques for Plain Mathematical Calculations

Incase if you find it difficult to derive the answer for difficult questions, practice some shortcuts like choosing an answer and working it backwards. This technique will save time and errors which occurs during long, complicated calculations. When it comes to this technique, start with the middle choice or answer. If the answer is not the same after working, the output will be higher or lower for sure. By doing this you will find you are getting closer to accurate answer

• Techniques to Solve Word Problems

There are some real life word problems or word problems in quantitative sections. These problems can be solved not only by plain mathematical formulae but logical reasoning is also required to solve them. Word problems will always be like “ Tom has 7 times as many crayons as Dick and 3 times as many as Harry. If Dick has less than 21 crayons, what is the maximum number of crayons that Tom can have? ” In order find the solution for problems of this kind, building an equation is a must. For example, for an example problem which was given above, make an equation where you assume Tom as A, Dick as B and Harry as C. This in turn will lead you to build an equation. The most important key while building an equation is to get familiar with identifying the least common factor or lowest common factor. This serves as a bridge between A, B and C in many a word problems.

• Techniques to Solve Geometry and Graphical Interpretation Problems

Some of the problems in problem solving part contain diagrams and graphical interpretations. The common error committed by many is that they judge the answers by relying on their vision. So they end up guessing wrong answers through visual judgments. The best way to choose the right answer is to read the question slowly while you review the diagram. While doing this spend 30 seconds in reviewing the diagram. Here comes the important role played by your pencil!  Draw rough sketches of these diagrams while calculating the answers and you will find that these diagrams contain some hidden information related to answers. When it comes to graphs remember your preparation in concepts like measurement of units, axis and labels. By the time you take up the test you will be able to interpret graphical data gradually, due to you getting used to mock tests which include so many graphical interpretations.

• Avoid Wasting Time on Easy Calculations

The best tactic to manage time in problem solving section is avoid wasting time in short calculations or repeating a calculation many times. This will help you to spend time on complicated problems like “which one of the following is true?” 

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Effective Problem-Solving Techniques in Business

Problem solving is an increasingly important soft skill for those in business. The Future of Jobs Survey by the World Economic Forum drives this point home. According to this report, complex problem solving is identified as one of the top 15 skills that will be sought by employers in 2025, along with other soft skills such as analytical thinking, creativity and leadership.

Dr. Amy David , clinical associate professor of management for supply chain and operations management, spoke about business problem-solving methods and how the Purdue University Online MBA program prepares students to be business decision-makers.

Why Are Problem-Solving Skills Essential in Leadership Roles?

Every business will face challenges at some point. Those that are successful will have people in place who can identify and solve problems before the damage is done.

“The business world is constantly changing, and companies need to be able to adapt well in order to produce good results and meet the needs of their customers,” David says. “They also need to keep in mind the triple bottom line of ‘people, profit and planet.’ And these priorities are constantly evolving.”

To that end, David says people in management or leadership need to be able to handle new situations, something that may be outside the scope of their everyday work.

“The name of the game these days is change—and the speed of change—and that means solving new problems on a daily basis,” she says.

The pace of information and technology has also empowered the customer in a new way that provides challenges—or opportunities—for businesses to respond.

“Our customers have a lot more information and a lot more power,” she says. “If you think about somebody having an unhappy experience and tweeting about it, that’s very different from maybe 15 years ago. Back then, if you had a bad experience with a product, you might grumble about it to one or two people.”

David says that this reality changes how quickly organizations need to react and respond to their customers. And taking prompt and decisive action requires solid problem-solving skills.

What Are Some of the Most Effective Problem-Solving Methods?

David says there are a few things to consider when encountering a challenge in business.

“When faced with a problem, are we talking about something that is broad and affects a lot of people? Or is it something that affects a select few? Depending on the issue and situation, you’ll need to use different types of problem-solving strategies,” she says.

Using Techniques

There are a number of techniques that businesses use to problem solve. These can include:

• Five Whys : This approach is helpful when the problem at hand is clear but the underlying causes are less so. By asking “Why?” five times, the final answer should get at the potential root of the problem and perhaps yield a solution.
• Gap Analysis : Companies use gap analyses to compare current performance with expected or desired performance, which will help a company determine how to use its resources differently or adjust expectations.
• Gemba Walk : The name, which is derived from a Japanese word meaning “the real place,” refers to a commonly used technique that allows managers to see what works (and what doesn’t) from the ground up. This is an opportunity for managers to focus on the fundamental elements of the process, identify where the value stream is and determine areas that could use improvement.
• Porter’s Five Forces : Developed by Harvard Business School professor Michael E. Porter, applying the Five Forces is a way for companies to identify competitors for their business or services, and determine how the organization can adjust to stay ahead of the game.
• Six Thinking Hats : In his book of the same name, Dr. Edward de Bono details this method that encourages parallel thinking and attempting to solve a problem by trying on different “thinking hats.” Each color hat signifies a different approach that can be utilized in the problem-solving process, ranging from logic to feelings to creativity and beyond. This method allows organizations to view problems from different angles and perspectives.
• SWOT Analysis : This common strategic planning and management tool helps businesses identify strengths, weaknesses, opportunities and threats (SWOT).

“We have a lot of these different tools,” David says. “Which one to use when is going to be dependent on the problem itself, the level of the stakeholders, the number of different stakeholder groups and so on.”

Each of the techniques outlined above uses the same core steps of problem solving:

• Identify and define the problem
• Consider possible solutions
• Evaluate options
• Choose the best solution
• Implement the solution
• Evaluate the outcome

Data drives a lot of daily decisions in business and beyond. Analytics have also been deployed to problem solve.

“We have specific classes around storytelling with data and how you convince your audience to understand what the data is,” David says. “Your audience has to trust the data, and only then can you use it for real decision-making.”

Data can be a powerful tool for identifying larger trends and making informed decisions when it’s clearly understood and communicated. It’s also vital for performance monitoring and optimization.

How Is Problem Solving Prioritized in Purdue’s Online MBA?

The courses in the Purdue Online MBA program teach problem-solving methods to students, keeping them up to date with the latest techniques and allowing them to apply their knowledge to business-related scenarios.

“I can give you a model or a tool, but most of the time, a real-world situation is going to be a lot messier and more valuable than what we’ve seen in a textbook,” David says. “Asking students to take what they know and apply it to a case where there’s not one single correct answer is a big part of the learning experience.”

Make Your Own Decision to Further Your Career

An online MBA from Purdue University can help advance your career by teaching you problem-solving skills, decision-making strategies and more. Reach out today to learn more about earning an online MBA with Purdue University .

If you would like to receive more information about pursuing a business master’s at the Mitchell E. Daniels, Jr. School of Business, please fill out the form and a program specialist will be in touch!

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