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Problem Solving

Concepts Tested on GMAT Problem Solving

The problems are based on various arithmetic and algebra math concepts, many of which are presented as word problems. There is no geometry, trigonometry, or calculus on the GMAT. All numbers used are real numbers; irrational numbers are not used.

• Arithmetic concepts on the test include number properties, fractions, percents, ratios, exponents and roots, and basic statistics. Also included are certain types of word problems such as rate and work, mixture, sets, probability, and basic combinatorics.
• Algebra concepts on the test include linear equations, basic quadratic equations, absolute values, and inequalities.

How to Approach GMAT Problem Solving

Read the question carefully and fully understand what is asked. Harder questions may be purposely worded in a confusing manner. For word problems, it is often helpful to translate the information presented into equations or in a tabular format. Make liberal use of the provided scratch board , as performing calculations in your head can lead to careless mistakes. Be systematic in your approach, organize the information logically, and clearly label everything. This becomes even more important as you tackle hard difficultly problems.

Before diving into calculations, examine the five answer choices for clues . Incorrect answers are typically not random numbers, but are instead created to ensnare test takers who make a careless mistake or fall into a common trap. Consider the format of the answers, so you know what you are working towards. Look for any similarities or differences amongst the available answers. If the answer choices are numbers that are far apart, some approximation may make for easier calculations .

Sample GMAT Problem Solving Question

Let’s try a sample problem. Attempt the problem on your own before viewing the answer and explanation.

A hospital purchased 50 stethoscopes and 270 boxes of tongue depressors from a medical supply company. If the price of each stethoscope was nine times the price of each box of tongue depressors, what percent of the total bill was the price of one stethoscope?

        (A) 0.8%         (B) 1.0%         (C) 1.25%         (D) 1.45%         (E) 2.0%

Explanation to Problem

There are three general approaches to this word problem: conceptual, algebraic, and plugging-in numbers. Let’s discuss each in turn.

Conceptual approach:

The conceptual approach, likely to be taken by advanced students, is the fastest. Since the question focuses on the price of a stethoscope, we can convert the total tongue depressor cost into an equivalent stethoscope cost. The price of each stethoscope is nine times the price of each box of tongue depressors (side note – we can safely assume that all stethoscopes are equally-priced and that all tongue depressor boxes are equally-priced). Thus nine tongue depressor boxes cost the same as one stethoscope.

Divide 270 (the number of tongue depressor boxes) by nine to calculate that the cost of these 270 boxes is equivalent to the price of 30 (270 ÷ 9) stethoscopes. Therefore, the total bill is equivalent to the cost of 80 stethoscopes: the 50 stethoscopes bought plus 30 more (representing the 270 tongue depressor boxes). As a result, one stethoscope is \(\frac{1}{80}\) of the total bill.

We now need to convert this into a percent. But first let’s review the other two approaches, to make the conceptual approach more understandable.

Algebraic approach:

This approach, likely to be taken by intermediate students, puts the conceptual approach into algebraic form. For this algebra word problem, let’s assign variables to the unknowns:

         S = price of one stethoscope          B = price of one box of tongue depressors

To calculate the total bill, multiply Price × Quantity for each item and then add the results. We are given the quantities, and can use our variables for the prices:

        Total bill = 50 S + 270 B

We are told that the price of each stethoscope is nine times the price of each box of tongue depressors. Using our variables, we can write an equation to express this relationship:

         S = 9 B

A common mistake is to write this equation backwards, as B = 9 S . Since stethoscopes are more expensive, however, we need to make the bigger value S equal to nine times the smaller value B . A small number B cannot equal a big number S times 9.

Since the question asks about stethoscopes and not tongue depressors, we want to get rid of B , the variable that we don’t care about. To do this, isolate B and substitute it away. Divide both sides of our equation by 9 (same as multiplying both sides by \(\frac{1}{9}\)).         \(\frac{1}{9}\) S = \(\frac{1}{9}\)(9 B ) = B

Now let’s do an algebraic substitution into the total bill equation:         Total bill = 50 S + 270(\(\frac{1}{9}\) S ) = 50 S + 30 S = 80 S

The question asks: the price of one stethoscope is what percent of the total bill ? We are looking for a percent, as further verified by the format of the answers. When calculating a percent, a good approach is to form a fraction with the “is” number on top and the “of” number on the bottom:         Percent = \(\frac{\text{is}}{\text{of}}\) = \(\frac{\text{stethoscope price}}{\text{total bill}}\) = \(\frac{S}{80S}\) = \(\frac{1}{80}\) (since the S variable cancels out)

We’ll convert this into a percent after reviewing the plugging-in numbers approach.

Plugging-in numbers approach:

This approach is likely to be taken by less-advanced students, but is actually a great approach for this problem. When the answers represent a ratio or percent, and we don’t have specific numbers provided within the problem, then a very good technique is to pick numbers to work through the math. The price of each stethoscope is nine times the price of each box of tongue depressors, so let’s pick easy numbers. We do not need to worry about whether the numbers are accurate in the real world, just whether the numbers meet the relationship described in the problem.

        Tongue depressor box = $1         Stethoscope = $9

Now calculate the total bill, using the price numbers we made up and the quantities provided in the problem.

        Total bill = 50 × $9 + 270 × $1 = $450 + $270 = $720

The question asks: the price of one stethoscope is what percent of the total bill? As mentioned in the algebraic approach, we can calculate the percent by forming a fraction with the “is” number on top and the “of” number on the bottom:         Percent = \(\frac{\text{is}}{\text{of}}\) = \(\frac{\text{stethoscope price}}{\text{total bill}}\) = \(\frac{$9}{$720}\) = \(\frac{1}{80}\) (since 9 goes into 72 eight times)

Converting the fraction into a percent:

There are several approaches to convert \(\frac{1}{80}\) into a percent. Worst case, we could do long-hand division. But there are a couple faster approaches.

Notice that \(\frac{1}{80}\) = \(\frac{1}{8}\) × \(\frac{1}{10}\). We recommend that students memorize the decimal equivalents of common fractions. So we should ideally know that \(\frac{1}{8}\) = 0.125. Multiplying by \(\frac{1}{10}\) is the same as moving the decimal one place to the left, resulting in 0.0125. Converting a decimal into a percent is done by moving the decimal two places to the right, so 0.0125 = 1.25%.

Another good shortcut takes advantage of the fact that a percent is equivalent to a fraction with a denominator of 100. How can we turn our denominator of 80 into 100? We can increase 80 by 25%, the same as multiplying 80 by 1.25. To leave the value of our fraction unchanged, we must multiply numerator and denominator by the same number.         \(\frac{1}{80}\) = \(\frac{1(1.25)}{80(1.25)}\) = \(\frac{1.25}{100}\) = 1.25%

Finally, if we are very short on time and don’t see an easy way to do the conversion, we could at least quickly eliminate three answers by recognizing that:         \(\frac{1}{100}\) < \(\frac{1}{80}\) < \(\frac{1}{50}\)  →  \(\frac{1}{100}\) < \(\frac{1}{80}\) < \(\frac{2}{100}\)  →  1% < \(\frac{1}{80}\) < 2%

Our correct answer has to be somewhere between 1% and 2%, leaving only answers C and D. As we have seen above, C is the correct answer.

GMAT Problem Solving (PS) Questions

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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?

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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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GMAT Quant Questions: Problem Solving

Note: GMAT Quant questions cover Problem Solving, and so much more. To get more math practice, try our free GMAT practice test with accurate score prediction and subject-by-subject performance breakdown.

On the GMAT Quantitative section, the Problem Solving questions are just the familiar five-choice multiple choice math problems you have seen on every standardized test since well before puberty.  Here, you have discovered a veritable treasure chest of Problem Solving sample questions.  

Below is a link to thirty-two different articles on this blog, each with at least two Problem Solving questions.  The sample GMAT Problem Solving questions are often at the top of the article, although sometimes they are further down in the text.  The total number of sample Problem Solving problems available from this page is far more than 37, the total number of math questions you will see on a full Quantitative section of the GMAT. 

In each blog, the solutions & explanations to the sample questions are at the ends of the articles.  (If the topic is less than crystal clear for you, you may find the article itself enlightening.)

1. Problems with Averages

https://magoosh.com/gmat/math/gmat-averages-and-sums-formulas/

2. Distance, Rate, Time

https://magoosh.com/gmat/math/word-problems/gmat-distance-and-work-rate-formula/

3. Permutations & Combinations

https://magoosh.com/gmat/math/gmat-permutations-and-combinations/

4. Factors & Prime Factorizations ( five practice PS questions at the bottom of the article )

https://magoosh.com/gmat/math/arithmetic/gmat-math-factors/

5. Advanced Geometric Solids

https://magoosh.com/gmat/math/geometry/gmat-math-advanced-geometric-solids/

6. Estimation questions

https://magoosh.com/gmat/math/the-power-of-estimation-for-gmat-quant/

7. Difficult Dice Questions

https://magoosh.com/gmat/math/basics/gmat-probability-difficult-dice-questions/

8. Difference of Two Squares

https://magoosh.com/gmat/math/algebra/gmat-quant-difference-of-two-squares/

9. Sequences ( five PS practice questions scattered through article )

https://magoosh.com/gmat/math/word-problems/sequences-on-the-gmat/

10. Remainders

https://magoosh.com/gmat/math/basics/gmat-quant-thoughts-on-remainders/

11. Work & Work Rate

https://magoosh.com/gmat/2012/gmat-work-rate-questions/

12. Circle & Line Diagrams

https://magoosh.com/gmat/math/geometry/circle-and-line-diagrams-on-the-gmat/

13. Polygons

https://magoosh.com/gmat/math/geometry/polygons-and-regular-polygons-on-the-gmat/

14. Set Problems, with Double Matrix Method

https://magoosh.com/gmat/math/word-problems/gmat-sets-double-matrix-method/

15. Set Problems, with Venn Diagrams

https://magoosh.com/gmat/math/word-problems/gmat-sets-venn-diagrams/

16. Scale Factor & Percent Change

https://magoosh.com/gmat/math/geometry/scale-factors-on-the-gmat-percent-increases-and-decreases/

17. Standard Deviation

https://magoosh.com/gmat/math/standard-deviation-on-the-gmat/

18. Radicals

https://magoosh.com/gmat/math/algebra/simplifying-radical-expressions-on-the-gmat/

19. Function Notation

https://magoosh.com/gmat/math/arithmetic/function-notation-on-the-gmat/

20. Algebraic Factoring

https://magoosh.com/gmat/math/algebra/algebra-on-the-gmat-how-to-factor/

21. Hard Factorial Problems

https://magoosh.com/gmat/math/arithmetic/gmat-factorials/

22. Backsolving from the answers

https://magoosh.com/gmat/math/gmat-plugging-in-strategy-always-start-with-answer-choice-c/

23. Distance in the x-y plane

https://magoosh.com/gmat/math/geometry/gmat-coordinate-geometry-distance-between-two-points/

24. Pythagoras !

https://magoosh.com/gmat/math/geometry/pythagorean-triplets-to-memorize-for-the-gmat/

25. Lines in the x-y plane

https://magoosh.com/gmat/math/geometry/gmat-math-lines-slope-in-the-x-y-plane/

26. Tricks for Calculating Combinations

https://magoosh.com/gmat/math/gmat-math-calculating-combinations/

27. Parallel & Perpendicular Lines and Midpoints in the x-y plane

https://magoosh.com/gmat/math/geometry/gmat-math-midpoints-and-parallel-vs-perpendicular-lines/

28. Probability: AND & OR Rules

https://magoosh.com/gmat/2012/gmat-math-probability-rules/

29. Probability: “at least” statements

https://magoosh.com/gmat/math/basics/gmat-math-the-probability-at-least-question/

30. Probability: counting problems

https://magoosh.com/gmat/math/gmat-probability-and-counting-techniques/

31. Hard counting problems

https://magoosh.com/gmat/math/word-problems/gmat-counting-with-restrictions/

32. Probability: geometric probability

https://magoosh.com/gmat/math/geometry/geometric-probability-on-the-gmat/

Also check out these GMAT Probability questions .

Other GMAT Practice Questions

Magoosh has practice materials for all of the GMAT question types in GMAT Quantitative  and in GMAT Verbal. Look at the table below, and click the links for more practice!

And make sure you do practice questions that cover the most common GMAT Quant concepts too.

Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as “member of the month” for over two years at GMAT Club . Mike holds an A.B. in Physics (graduating magna cum laude ) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike’s Youtube video explanations and resources like What is a Good GMAT Score? and the GMAT Diagnostic Test .

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One response to “GMAT Quant Questions: Problem Solving”

this work is fantastics job, i need more of the solved problems

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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GMAT Prep Online Guides and Tips

The best gmat study guide: format, tips, and practice.

In this GMAT study guide, I’ll walk you through the GMAT study process from start to finish. First, I’ll talk about why studying for the GMAT is worth the time and effort. Next, I’ll talk about the GMAT itself – the format of the test and what it covers. Then, I’ll give a brief overview of each of the sections of test, discussing the content and format of each.

After that, I’ll move into talking about how to set a goal score, create your GMAT study plan, and stick to it. Finally, I’ll talk about the practice itself. I’ll tell you where to find study materials and give you some tried and true study strategies for both the test as a whole and each individual section.

By the end, you’ll have a clear idea of where to start to study for the GMAT.

Why Should I Study for the GMAT?

Studying for the GMAT is a big commitment. Why should you do it? What will studying accomplish? Here are three important ways that studying for the GMAT can help you achieve your goals.

Not sure how or what to study? Confused by how to improve your score in the shortest time possible? We've created the only Online GMAT Prep Program that identifies your strengths and weaknesses, customizes a study plan, coaches you through lessons and quizzes, and adapts your study plan as you improve.

We believe PrepScholar GMAT is the best GMAT prep program available , especially if you find it hard to organize your study schedule and don't want to spend a ton of money on the other companies' one-size-fits-all study plans.

#1: Raise Your Score

Using a GMAT study guide with clear goals and objectives is the best way to raise your GMAT score. If you’re looking to achieve a certain goal score, setting up a clear and achievable GMAT study plan will help you reach your goals.  Without a clear GMAT study guide, you’ll likely struggle to find time to study amongst all of your responsibilities. It’ll also be hard to ensure that you’re covering all the topics you need to improve on.

#2: Build Your Skills in Different Areas

When you study for the GMAT, you help to build your skills in different areas.  The GMAT tests many different skills across a wide variety of content areas. Very few test-takers are good at every single skill when they start thinking about taking the GMAT. By studying, you’ll be able to improve in areas of weakness and strengthen the areas that you’re already doing well on.

#3: Feel Confident on Test Day

Using a GMAT study guide to plan out your GMAT prep will help you feel more confident on test day. You’ll walk into the test center knowing what types of questions will be on the test, what the test format will be like, and how much time you’ll have, so that you’re comfortable and ready to go.

What’s on the GMAT, Anyway?

The GMAT is made up of four total section and has a total exam time of three hours and 30 minutes. Let’s look at what’s covered on each section of the test.

*Total Score is made up of the scaled scores from your Verbal and Quantitative sections. For more info, check out our GMAT Total Score guide .

Analytical Writing Assessment

The GMAT Analytical Writing Assessment tests your ability to think critically and clearly communicate your ideas.

During this section, you’ll be asked to analyze the reasoning behind a given argument and write a critique of that argument.

Integrated Reasoning

The GMAT Integrated Reasoning section is the newest section of the GMAT. It’s designed to measure skills that you’ll need to do well in today’s advanced, data-driven world.

The Integrated Reasoning tests your ability to evaluate information given in multiple formats and from multiple sources with four question types: graphics interpretation, two-part analysis, table analysis, and multi-source reasoning.

Quant Section

The GMAT Quant section tests your ability to analyze data and draw conclusions using reasoning skills.  It  covers basic math concepts, such as arithmetic, algebra, and geometry. Contrary to popular belief, the GMAT quant section doesn’t test advanced math concepts.

There are two types of questions on the GMAT quant: data sufficiency and problem solving.

Verbal Section

The GMAT Verbal section tests your ability to read, understand, evaluate, and edit different types of written material.

There are three types of questions on the GMAT verbal: reading comprehension, critical reasoning, and sentence correction.  The reading comprehension question type tests your ability to read and understand written material. The critical reasoning question type tests your ability to reason and evaluate arguments. The sentence correction question type tests your ability to identify errors and correct material to standard written English.

Creating Your GMAT Study Plan

Now that you know more about the GMAT, let’s talk about how you can create the best GMAT study plan to meet your goals.

Step 1: Set Your GMAT Goal Score

First, put together a list of all the business school programs that you’d like to attend. When you’re putting together your list, think about why you would like to attend each of these programs.

Next, research the average GMAT scores of the business schools that you want to apply to. You can find this information in a number of places. Most schools share this information on the program’s admissions page. You can also try calling the admissions department if you can’t find the info there. Other third party sources, like US News, also list the average GMAT scores of many schools.

Add the average GMAT scores for each school to your list of business school programs that you’re interested in. Find the highest average GMAT score of all the programs.

You want to set a score goal that’s about twenty points higher than the highest average GMAT score. This helps make sure you’ll be above the acceptable score range for all of your programs.

Step 2: Take a Practice Test

Your next step is to take a GMAT practice test if you haven’t already done so. Taking a GMAT practice test helps you get an idea of where you’re currently scoring and helps you understand what taking the test is actually like.

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The best way to do this is to download the free GMATPrep software so you can take an official practice test.

Try to replicate the exam day as closely as possible. So, make sure you’re taking the test timed, in one sitting, and in a quiet place with few interruptions. This helps ensure you get the most accurate practice score.

You’ll automatically receive all of your scores, except for the score for you Analytical Writing Assessment. For more information about what a GMAT total score is, check out our guide (link).

Step 3: Analyze Your Weaknesses

Understanding your weaknesses is a great way to make substantial gains to your GMAT score.

Use your practice test scores to get a better picture of your strengths and weaknesses as a GMAT test taker. Try to identify patterns: did you miss every sentence correction question? Are you better at the Verbal section than the Quant section? Did you miss every single Integrated Reasoning question? Asking and answering these questions will help you focus your prep by highlighting the sections you need to spend the most time on.

Step 4: Figure Out How Many Hours You’ll Need to Study

Now that you’ve figured out your baseline score, compare that to your goal score. Figure out how many points you are away from meeting your goal score.

I’ve included estimates of approximately how many hours you need to study in order to increase your score by a certain number of points.

• 0 – 50 points, 100 hours
• 51 – 100 points, 120 hours
• 101 – 150 points, 160 hours

Step 5: Create Your GMAT Study Schedule

Now that you’ve figured out how many hours you need to study total, figure out how many hours each week you can study.

Be realistic about this. You want your study time to be productive. You also want to make sure you’re not neglecting your other work or responsibilities. If you set a practice schedule that’s too packed, you might end up frustrated and burned out.

Divide the total number of hours you need to study by the number of hours you can study each week. That’s the number of weeks you need to study.

So if you need to study 120 hours and you can study for 10 hours each week, you will need to study for 12 weeks.

You may also want to build in time for retakes. You can take the GMAT up to five times in a 12 month period, but you have to wait for at least 16 days between exams.

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If you choose which schools to send your test scores before you take the GMAT, the schools will receive your scores in less than 20 days. To be safe, schedule your GMAT at least three weeks before application deadlines.

Step 6: Set Goals for Your Study Periods

Setting small goals for yourself is a great way to keep yourself on track and to make yourself feel good about your accomplishments.

You can set daily, weekly, or monthly goals (or all of the above). These goals might be simple (practice 50 math questions per week) or more complex (master graphics interpretation strategies).

Goal-setting will keep you accountable and will keep you on the right path with your practice.

Step 7: Track Your Progress

Scheduling and taking regular practice GMATs is a great way to monitor your progress.

Compare your scores to your original test. What sections did you improve on? Did you do worse on any section? What section is slipping through the cracks of your study plan?

Adjust your goals as needed based on your progress on practice tests. Maybe you were doing great on sentence corrections one week, but started to struggle the next. You could add a goal to your study plan that’ll remind to focus on that topic.

Finding GMAT Practice Materials

An important part of any GMAT study guide is great practice materials.

There are two main types of GMAT practice materials. Official GMAT prep materials are written by GMAC, the company that writes the GMAT. Unofficial GMAT prep materials are written by third-party companies that have extensively studied the GMAT and write their own test prep materials and questions.  Official GMAT materials are the best practice tools, since they include actual retired GMAT questions , but unofficial materials can be helpful as well, especially for learning strategies and review content.

To get you started, we’ve rounded up some of the best options for both types of prep materials.

Official GMAT Prep Materials

Official practice materials should be an important part of your prep. Practicing with official materials ensures that you’ll be working on questions that are just like what you’ll be seeing on test day.

GMATPrep Software

This free, online software gives you access to two full-length CATs, with the option to purchase up to four more. The “Exam Mode” of this software realistically simulates test day, which is great for building up your comfort with the exam. While the free product doesn’t have many practice questions, you can purchase additional question packs or use another resource in conjunction with this software.

The Official Guide for GMAT Review Set

This three-book set contains guides for the Verbal and Quantitative sections, as well as an overview of the entire test. It comes with access to over 900 official practice questions, which makes it an invaluable resource. Official practice questions are the best type of question you can practice, as they’re written by GMAC, who also writes the GMAT. While these guides don’t offer particularly comprehensive content reviews, they’re a great resource to use during your practice.

Unofficial GMAT Practice Tests

There are plenty of options for other unofficial GMAT practice tests if you’ve used up the official options. It’s important to take online tests whenever possible so that you can keep building your familiarity with the test. Here are two great resources for free CATs:

Veritas Prep

Veritas Prep offers one free GMAT practice test with explanations . If you’d like, you can purchase 6 more tests for $49. You can take the test with normal time, or you can add extra time. Veritas Prep is known for having accurate GMAT questions and in-depth explanations.

Kaplan offers two types of free online GMAT practice tests : self-proctored and instructor-proctored. For the self-proctored test, you’ll receive your scores and answer explanations to peruse at your leisure. For the instructor-proctored exam, you’ll get your scores, and then work with an instructor in real-time online to get answer explanations. Kaplan is generally fairly accurate, but does have some problems with having questions that are either a little different in format or a little off from GMAT core content.

Other GMAT Practice Resources

There are tons of different GMAT study resources out there, besides the ones offered online. In this section, I’ll offer some recommendations about other resources you can use in your GMAT prep.

GMAT Prep Books

One of the most popular options for GMAT books is the Manhattan Prep series , which provides a comprehensive overview of all topics seen on the GMAT. The 10 books that make up this bundle are designed to provide a substantial learning impact for students by helping them develop the knowledge, skills, and strategic thinking they need to do well on the test.  These books are great for developing deep knowledge of the content on the GMAT, and come with a year-long subscription to high-quality online practice tests.

If those aren’t right for you, there are a ton of other options for GMAT test prep books. Check out our complete guide to the best GMAT books  for more ideas.

There are lots of GMAT forums out there. These online message boards provide a place for past, present, and future test-takers to gather, share tips and tricks, and pool resources. Beat the GMAT and GMAT Club are great places to find information on strategies, reviews of prep materials, and access to other free resources, like downloadable question banks or flash cards.

The 4 Most Important GMAT Study Tips

Even if you have the best tools in the world, studying for the GMAT won’t get very far if you don’t put in the time and effort to study well. In this section, I’ll offer some tips for how you can study well for the GMAT, maximizing your time and effort to achieve your goal score.

Practice as Realistically as Possible

Simulate real test conditions as much as possible. This means doing practice on the computer to familiarize yourself with the test’s format. It also means practicing without a calculator, since using one isn’t allowed on the test. Try to always work in a quiet place with few distractions. Along the same lines, make sure you’re practicing with real (or accurate) questions that mirror the content you’ll see on the test.

Eliminate Distractions

Try to eliminate distractions while you study. Turn your cell phone to silent. If you’re like me and find yourself compulsively checking Facebook every five minutes, use a blocker like SelfControlApp to make sure you turn off access to social media during your studying.

Analyze Your Performance and Adjust Accordingly

As I mentioned before, set goals and stick to them. Use goals as a way to monitor your day-to-day progress, while using practice tests to assess larger arcs of performance. After you take a practice test, or meet or fail to meet a goal, make adjustments to your study schedule to make time for sections you need more work on and lessen the time you’re spending on sections that you’ve already mastered.

Learn the Test

Spend time familiarizing yourself as much as possible with the GMAT. Learn the question types asked on each section. Know the format of the test and the time you’ll have on each section. Use CATs to practice using the tools and functions that the real test will have. Doing these things will increase your confidence with the GMAT and reduce your anxiety on test day.

Review: The Best GMAT Study Guide

The GMAT is a long and difficult test, with four separate sections testing different types of content. However, you can increase your chances of achieving your goal GMAT score by crafting and executing a strong GMAT study guide.

Part of creating the best GMAT study guide for your testing needs is using high quality practice resources, so make sure to vet your practice materials to ensure their quality before you invest in them. Finally, make sure that you are preparing effectively by following my tips about how to study for the GMAT.

What’s Next?

Ready to craft your ultimate GMAT study plan? In our guide to writing a GMAT study plan , we offer four sample study plans designed to boost your score based on your individual test goals. Check out our guide to GMAT study plans to get started on yours.

Looking for those high quality GMAT practice books? There are tons of materials out there for you to peruse. You can choose GMAT prep books based on your strengths, weaknesses, and preferences as a test taker. Use our best GMAT Books guide to decide what prep books to buy.

Registering for the GMAT can be more complicated than you anticipate. If you’re ready to sign up for the GMAT, our step-by-step guide for registering for the GMAT will help walk you through the process.

Was this helpful? Sign up for FREE GMAT and MBA guides!

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Author: Hayley Milliman

Hayley Milliman is a former teacher turned writer who blogs about education, history, and technology. When she was a teacher, Hayley's students regularly scored in the 99th percentile thanks to her passion for making topics digestible and accessible. In addition to her work for PrepScholar, Hayley is the author of Museum Hack's Guide to History's Fiercest Females. View all posts by Hayley Milliman

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GMAT Problem Solving Questions With Answers

Problem Solving questions constitute a major chunk of the Quant section of the GMAT. Of the 31 questions that appear in this section, you can expect close to 50% of the questions from problem-solving. In this article, we will be looking into –

What are GMAT Quant Problem Solving Questions?

• 3 examples of GMAT Problem Solving Practice Questions
• 5 tips that can help you ace these questions.

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Problem Solving or PS questions are questions that have a question followed by five options. They are very similar to any MCQ question that we come across in our school or university examinations. You need to solve the question and arrive at the answer and mark the correct choice.

There is only one correct answer in Problem Solving Questions.

Problem Solving questions are considered easier than Data Sufficiency questions because they are straightforward. Having said that, a preparation without a proper plan might prove disastrous for these questions.

Let us now take a look at a few Problem-Solving questions to get you started.

Examples – GMAT Problem Solving Questions

Question 1:.

If a regular unbiased die is rolled twice, what is the probability of getting a sum greater than 10 in the two rolls?

In probability, the probability of an event E = The number of favourable outcomes / Total number of outcomes

The first step is to calculate all favourable outcomes.

Let {x,y} represent the two rolls.

For getting a sum greater than 10, we can get a sum of 11 it a sum of 12.

Now, for a sum of 11, we can have these cases – {5,6}, {6,5}

For a sum of 12, we can have these cases – {6,6}

Hence, there are three favourable outcomes.

Total number of outcomes = 6*6 = 36

Hence, probability = 3/36 = 1/12.

Question 2:

The length of the equal sides of an isosceles triangle is 6 cm. What is the maximum possible area of the triangle(in square centimetres)?

Let us assume that one of these 6 cm sides is the base and the angle that the other 6 cm side makes with the base is k degrees.

Now, we know that the area of a triangle whose 2 adjacent sides are known and the enclosed angle is known can be calculated as:

Area = (1/2)*a*b*sin(k)

a = First side

b = Second side

k is the angle enclosed.

Now, a and b are fixed as 6 cm each

If sin k is maximum = 1, the value will be maximum.

Hence, the maximum possible area = (1/2) x 6 x 6 = 18

Question 3:

If a set A has 16 distinct elements all of which are integers and set B necessarily has the square of all elements of set A, what can be the minimum number of elements in set B?

If all 16 elements in A are distinct, say 1, 2, 3, …., 16, then B also has 16 elements 1, 4, 9, ….., 256.

However, to reduce the number of elements of B, we need to have as many elements as possible in A that also has their negative counterpart in A. For example, if 2 is an element, -2 should be an element as well. As a result, if 4 (square of both 2 and -2) is present in B, it will account for 2 elements in A.

Hence, we can have 8 positive numbers in A and their corresponding negative numbers in A. In this way, we can say that B will have a minimum of 8 elements.

Hence, the minimum possible number of elements in B is 8.

Though these examples provide a good sense of what type of GMAT Problem Solving questions you can expect, in no way do they represent the exhaustive list of concepts required for the Quantitative section of GMAT.

Tips to keep in mind:

• Try to take some time out from easy Problem Solving questions so that you can use that time to solve tricky Data Sufficiency questions. Data sufficiency questions usually take more time to solve than Problem Solving questions.
• Do not get stuck in a question for long. If you find yourself trapped in a question for long, take a guess and move on.
• Read the units carefully.
• Look out for negation words. For example: Which of the following are NOT possible values of x?
• Some questions can be solved faster by the use of options. Make sure you don’t solve these questions in a conventional way.

You can check out the Free GMAT Daily Targets on our platform .

Also, check out the Free GMAT Verbal Tests and Quant Tests .

If you are starting your GMAT preparation from scratch, do check out GMATPOINT.

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Hope this article was helpful. Wish you all the best for the GMAT.

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GMAT Critical Reasoning – The Foundation of the Exam

Chris Kane - Menlo Coaching

Chris Kane is a mba.com Featured Contributor.

No skill is assessed more on the GMAT than critical thinking. In one form or another, every question type – from Sentence Correction to Problem Solving – is cleverly evaluating your ability to remain critical and find flaws in your own approach to a question or within the information provided in that question. Why? Because the best managers and business executives are those who can quickly isolate problems and fix them efficiently and effectively.

The Critical Reasoning question type is, of course, the ultimate assessment of this essential business skill. GMAT Critical Reasoning questions are designed to evaluate a specific set of attributes relating to logic, and most students preparing for the test have never been exposed to this type of argument analysis. Broadly speaking, there are 3 types of Critical Reasoning questions you will encounter on the GMAT Verbal section:

• Those in which you must attack a given argument or plan (called the stimulus) and then find the answer choice that exposes a flaw or improves a flaw within that stimulus.
• Those in which you must analyze and describe the line of reasoning used within the stimulus.
• Those in which you must supply a valid conclusion based on the information given in the stimulus.

For type 1 questions, there are several important subtypes that you will see described by test prep companies: strengthen, weaken, assumption, useful to evaluate, and explain the paradox. Type 2 questions are most commonly called method of reasoning questions (usually boldfaced questions), and type 3 are commonly referred to as inference or conclusion questions. Note: well over 75% of the Critical Reasoning GMAT questions you will see on your exam are type 1, so we will focus mainly on the strategies for that common type in this article.

Best Practices for GMAT Critical Reasoning

To succeed in Critical Reasoning, you must develop a structured set of best practices that help you quickly maneuver through the different tricks and traps you will encounter on these questions. Some of these tips, such as reading the question stem first, are universal across different test prep curricula, while others are more sophisticated.

1. Read the Question Stem First

Since the mindset and strategies required for these three types of Critical Reasoning questions (and even between the subtypes in category 1) are so different, it is essential that you read the question stem first to determine which type of question you are facing. As an example, consider the following two question stems, which can easily be confused:

• Which of the following most supports the argument above?
• Which of the following is most supported by the argument above?

In the first question stem, you are dealing with a strengthen question. You need to attack the given argument or plan and then find a new piece of information in the five answer choices that necessarily improves the given argument or plan.

In the second question stem, your approach is completely different! You take everything in the stimulus as fact, and then determine which of the answer choices is a valid conclusion based on that given information.

If you don’t read the question stem first, you are wasting valuable seconds in your initial reading of the given stimulus because you don’t know your goal, and you will thus face time pressure on the verbal section. Additionally, if you don’t categorize the question correctly, you are doomed to get it wrong, and GMAT question writers purposefully make this task difficult.

2. Master the Art of Deconstructing Arguments

Another core skill tested on the GMAT is your ability to contend with abstract presentation of information and concepts. Many Critical Reasoning questions contain extremely complicated arguments that are both abstract and difficult to comprehend.

One of the big mistakes students make in attacking Critical Reasoning questions is that they go to answer choices before they fully deconstruct and understand the given stimulus. Piling on additional information to something you don’t fully understand is a common mistake students make on the GMAT generally – don’t go to answer choices until you understand the given information and the goal of the question!

In our Menlo Coaching GMAT curriculum , we put a huge emphasis on teaching students how to properly deconstruct arguments. This is best done by reading the full argument (for type 1 and type 2 questions, in which you are presented with a full argument in the question stem) and then isolating the conclusion. To make sure you have actually found the proper conclusion, you “Ask Why?” to that conclusion and see if the question leads back to the premises within the argument. Once you have done all of this properly and fully understand the given stimulus, you should then move to the next step in your structured best practices.

3. Attack (and Anticipate)!

So at this point, you have categorized the question type and fully deconstructed the given stimulus; now the real game of GMAT Critical Reasoning begins!

For all type 1 questions, you will have a full argument or plan in the stimulus, and you need to attack that stimulus, finding any flaws or common fallacies within the line of reasoning. In 20 years of preparing students for this question type, I have noticed one universal attribute among the “masters” of GMAT Critical Reasoning: they find the flaws on their own first and then evaluate the answer choices. To some this may seem counterintuitive (shouldn’t you leverage the answers first?), but the reality for all type 1 questions is that the answer choices are more your enemy than your friend.

In general on the GMAT, an essential best practice is to leverage all answer choices and use them actively, but Critical Reasoning answer choices are notoriously manipulative. Incorrect answers tempt you with ideas and “flaws” that pollute your brain and keep you from isolating the true issues in the argument. By attacking the argument before digging into answers, you are in charge of finding the flaws (and you will hone this skill with lots of practice) and can avoid this “polluting of the mind” by clever incorrect answers.

When you do anticipate flaws in the stimulus (often called “pre-thinking” in test prep curricula), it is essential that you do so broadly: don’t anticipate exactly how the answer choices might relate to the flaw, but find the core issues in the argument that should be addressed within one of the answers, which often does so in an obtuse or confusing way. On the hardest type 1 questions, you will likely need to use some hints from the answers about what to consider in the stimulus, but you must do that carefully while you sort through a collection of tasty trap answers.

Importantly, this type of anticipation is really only used for type 1 questions. For method of reasoning questions, you will deconstruct the argument and perhaps find some flaws, but you need to use process of elimination and compare answers to see which one is accurately describing the argument or the boldfaced portions of that argument. For inference/conclusion questions, you cannot anticipate what valid conclusion the question writers might provide, so again you need to attack each answer choice using process of elimination until you find the one answer that is a valid conclusion.

In summary, if you want to improve accuracy and speed in GMAT Critical Reasoning, you must get comfortable attacking arguments on your own and recognizing the common logical fallacies found in these questions. In no particular order, here are some of the most common fallacies you will encounter in GMAT Critical Reasoning practice questions and on your exam:

• Mistaking Correlation for Causation
• Generalization
• Numerical Data Flaws (using absolute number data when you should use percentage data, improper use of statistics, etc.)
• Past Trends Don’t Guarantee Future Trends
• Baseline Assumptions (forgetting about starting points and what might have been true in a previous time frame)

Make sure you understand these flaws deeply and get skilled at recognizing them in a variety of scenarios and presentations.

4. Analyze the Answers (and be ready for the more “sinister” tricks and traps in GMAT Critical Reasoning).

Now, you are fast at categorizing the question and deconstructing the stimulus. You have mastered the common logical fallacies used on GMAT Critical Reasoning questions and you are good at attacking arguments on your own. That means you will get most GMAT Critical Reasoning questions correct, right? Sadly, that is not enough!

The additional mechanisms used to make these questions hard are the most sinister and difficult to handle. These traps are mainly assessing who is paying careful attention to details and making sure their mind does not wander (again important skills in business!):

• Wordplay. Wording scenarios and clever language construction are used to elicit misinterpretation and misreading by the test-taker. Often this involves negation or other forms of abstract wording.
• Misdirection. Question writers insert captivating information (what I often call the “shiny penny”) to draw your focus away from what really matters, which may be quite boring..
• Mental Inertia. This is a form of misdirection in which question writers use topics for which everyone has deeply preconceived notions, but the answer is contrary to what you expect.
• Word Shifts. You will commonly see subtle word shifts that create gaps or flaws within an argument. As I joke in my classes, there is no such thing as “synonyms” in Critical Reasoning. If a word has been changed between premises or between premises and the conclusion, it is probably creating a gap within the argument.

Seeing through this type of difficulty and avoiding these common traps and tricks comes through doing lots of high quality official GMAT Critical Reasoning practice questions. After you get burned by these different cons enough times, you start to see the traps quickly and your percentile in GMAT Critical Reasoning will jump dramatically. Pattern recognition through completion of a high volume of official problems is essential to success in training for Critical Reasoning.

GMAT Critical Reasoning Practice Question

To conclude this article, let’s apply these best practices to one retired official Critical Reasoning question. Take around 2 minutes and try to solve the question on your own:

The program to control the entry of illegal drugs into the country was a failure in 1987. If the program had been successful, the wholesale price of most illegal drugs would not have dropped substantially in 1987.

The argument in the passage depends on which of the following assumptions?

A. The supply of illegal drugs dropped substantially in 1987.

B. The price paid for most illegal drugs by the average consumer did not drop substantially in 1987.

C. Domestic production of illegal drugs increased at a higher rate than did the entry of such drugs into the country.

D. The wholesale price of a few illegal drugs increased substantially in 1987.

E. A drop in demand for most illegal drugs in 1987 was not the sole cause of the drop in their wholesale price.

Explanation

This problem is a great example of the wordplay and misdirection that I highlighted previously. The argument itself isn’t that difficult to understand but the answers are manipulative and the wording tricky. Let’s apply all the previously discussed GMAT Critical Reasoning tips in a methodical way to find the correct answer:

• Categorize. The question is clearly an assumption question, a type of strengthen question in which you must isolate a necessary premise in the 5 answer choices. The correct answer will necessarily improve the quality of the argument.
• Deconstruct. Since this is a relatively short and simple argument, it is easy to deconstruct. You should first isolate the conclusion – ”The program to control entry of illegal drugs was a failure in 1987” – and then “ask why?” to build back any given premises. Why was it a failure? Because if it had been a success, the wholesale price would not have dropped substantially in 1987. As is often true in assumption questions, you must deal with negation both in the given argument and in some of the answer choices. To help better understand the argument, simplify the given premise using affirmative language (but be careful not to change the meaning!). “Because if the program had been a success, the price would have remained the same or gone up (or perhaps just dropped a little)”
• Attack and Anticipate. This argument presents a classic flaw in which alternative explanations are ignored. The argument relies on the idea that if the price went down substantially, it must have been because supply increased from the entry of illegal drugs and thus the program failed. But wait a second what else could have caused the price to drop substantially? If demand for illegal drugs dropped in 1987, then the price could have gone down even if the program was successfully preventing the entry of drugs. Alternatively, domestic production could have increased the supply of available drugs and the price could have gone down even with successful control of illegal entry from other countries. With those two flaws in mind, carefully assess the answers.
• Analyze the Answers (while looking out for wording tricks and more sinister traps).

(A) The correct answer should support the idea that the program was a failure. If anything, this statement does the opposite! If the supply dropped, then likely the program was a success, not a failure (but we don’t even know because the decrease in supply could have been related to domestic sources). On most strengthen questions, at least one trap answer will weaken the argument, particularly when negation is present, because test-takers get confused about their goal with the argument.

(B) This tricky incorrect answer contains the negation you often see in GMAT Critical Reasoning assumption questions. Another common Critical Reasoning tip you will see across most test prep curricula is the assumption-negation technique. In short, this technique can be used to deal with difficult negation in answer choices for assumption questions. If you negate an essential premise (which is the correct answer in an assumption question) then it should destroy the argument. This allows you to take any answer choice presented negatively and read it affirmatively to see if it destroys the argument. Let’s do that here:

The price paid for most illegal drugs by the average consumer did not drop substantially in 1987.

So if the price paid did go down, this supports the idea that the program was a failure! If it was correct, this negated version should destroy the argument. The human brain does not deal with negation well, so it is much easier to read answers like this affirmatively to see if they destroy the argument. Both of the first two answers are wrong essentially because they do the opposite of what they should. Also, you should note that this answer is about the price paid by consumers while the argument is using wholesale prices for its evidence a classic word shift!

(C) To make the argument that the program was a failure, you do not need to know that the domestic rate increased more than the foreign entry rate. The program would be a failure even if the domestic rate increase was less than the foreign entry rate increase. This comparison is irrelevant to the given conclusion but since it broadly addresses the domestic vs. foreign issue that you should have considered after your initial reading, some people will still pick it.

(D) The given argument involves “the wholesale price of most illegal drugs” while this answer just discusses a few illegal drugs. A few illegal drugs could increase while most drop with no effect on this argument. Note: if anything, this statement would again weaken the conclusion when we are trying to improve it. An increase in prices suggests the program might have been a success, not a failure.

Correct Answer

(E) Jackpot! Since this answer is presented negatively, let’s apply the assumption-negation technique and see if this destroys the argument.

A drop in demand for most illegal drugs in 1987 was not the sole cause of the drop in their wholesale price.

So, if a drop in demand WAS the sole cause of the drop in their wholesale price, this argument is completely destroyed because the price drop was not due to a failure of the drug entry program. This correct answer essentially removes a flaw, that if true, would be very problematic for the given conclusion.

Final Takeaways

To succeed in GMAT Critical Reasoning you need to follow a structured set of best practices. As you can see from this one example, the difficulty can be more from the negation and wording than from a difficult-to-find flaw or confusing argument. The most important skills to develop while training with official GMAT Critical Reasoning practice problems are the following:

• Quickly be able to deconstruct and understand given arguments.
• Attack arguments efficiently and be able to find all broad flaws within a line of reasoning on your own.
• Learn how to contend with the difficult tricks and traps relating to wordplay and abstract presentation.

When those skills are mastered, you will see your CR percentile jump considerably AND you will be able to complete CR questions faster, allowing for less time pressure on the GMAT verbal section.

Chris Kane is an mba.com Featured Contributor.  

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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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