quantitative problem solving questions

GMAT Quant Questions: Problem Solving

Note: GMAT Quant questions cover Problem Solving, and so much more. Be sure to use our GMAT Practice Test to test your knowledge of these concepts.

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 .

Addendum to the table: A special note on Sentence Correction questions

Sentence Correction questions are the very shortest questions on the test, both in terms of word count and time. Ideally, you should complete any SC question in less than one minute. Make sure you set your speed for this question type carefully. And be aware that Sentence Correction questions do NOT have their own subsection in GMAT Verbal; instead, SC is mixed in with Critical Reasoning and Reading Comprehension on the GMAT.

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 .

View all posts

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

Free GMAT Test Questions

Welcome to our Question Bank!

You have not answered any question so far. There are 50 free practice questions in our database in total, which you can answer and will improve your skills.

You can answer all questions in a row (click on "All Questions") or only all questions of a particular section (click on that Section) or a single selected question (click on that Question).

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Quantitative reasoning - problem solving, quantitative reasoning - data sufficiency, verbal reasoning - critical reasoning, verbal reasoning - reading comprehension, verbal reasoning - sentence correction.

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What is the GMAT Quantitative Reasoning Questions Exam Structure?

The quantitative reasoning section tests your numerical literacy and mathematical abilities, such as solving quantitative problems and interpreting graphical data. It consists of 31 multiple choice questions, which should take 62 minutes (2 minutes per question) to be completed.

The quantitative reasoning section of questions consists of data sufficiency and problem-solving questions.

1. Data Sufficiency Questions Each Data sufficiency question is made up of a question and two statements. To answer a question, one should first identify the statement that provides information relevant to the question, and then eliminate all the other possible answers by using math knowledge and other everyday facts. There will be 14 to 15 questions on data sufficiency in each quantitative section.

2. Problem-solving Questions Each Problem-solving question includes a question section and five possible answers to choose from. The questions are designed to assess your use of logic and analytical reasoning to answer quantitative problems.

What are the Skills and Strategies to Excel in Quantitative Reasoning Questions?

Math skills.

Quantitative Reasoning questions call for the application of math knowledge to solving problems. Such mathematical skills include:

Basic arithmetic including fractions, integers, powers and roots, and statistics and probability.
Algebraic topics such as variables, functions, and solving equations.
Word problems such as algebraic and geometric principles and blending arithmetic used to solve problems.
Geometry, particularly geometrical objects such as triangles, circles, quadrilaterals, solids, cylinders, and coordinate geometry.

Essential Strategies in Problem Solving Questions

Always check your onscreen timer. Apply caution while solving questions but don’t waste too much time verifying answers; strive to complete a given section.
If you find a question difficult or time-consuming, try to eliminate answer choices that might be outrightly wrong and select your best choice from the remaining ones.
Study each question in depth to ascertain what is being asked. For example, you may need to come up with some equations.
Solve the questions by writing to limit errors. An erasable tablet will be provided at the test center.
For the data sufficiency questions, ascertain whether the question requires only one value or a range of values. Moreover, avoid unnecessary assumptions about geometrical figures, as they are not usually drawn to scale.
Go through the answer choices before answering a question to get the gist of what kind of answer choice structure you are required to present. Moreover, some questions require simple approximation presentations, which may require little mental activity rather than long computations.

Questions Answered by our Users

Satisfied customers, preparation platform by review websites, some free exam-style gmat practice questions offered by analystprep, gmat quantitative problems, division & factoring.

When a number $b$ is divided by $a$, the remainder is 12. Given that $\frac{b}{a}=7.15$, what is the value of a?

The correct answer is: C)

The result 7.15 due to division gives us the quotient 7 and the remainder 0.15. Therefore, $\frac{12}{a} =0.15$ implying that $a=\frac{12}{0.15}=80$.

Descriptive Statistics

Dre has seven French tests this semester that is each scored out of a maximum of 100 points. If his average score on the first five tests was 87, what is the minimum score he could get on the sixth test and still be able to maintain his 87 average through all seven tests?

The correct answer is: A)

If the average score on Dre’s first five tests is 87, the sum of the first 5 scores is $5 × 87 = 435$.

To maintain a score of 87 for all 7 tests, the total score required would be $7 × 87 = 609$.

The maximum score Dre could get on the seventh test would be 100, so $609 – 435 – 100 = 74$ would be the minimum score he could get on test 6 and still maintain his 87 point score average.

Linear Algebra

Scott began losing weight at a constant rate five months ago and today weighs 25 pounds less than he weighed then. Concurrently, his brother Karl has also been losing weight at three times the rate of Scott. If Karl weighed the same weight two months ago that Scott is today, and the two brothers weigh a combined 450 pounds today, what was Scott’s weight five months ago?

So, Scott’s weight today $= s−25$.

Karl’s weight loss rate is three times that of Scott, i.e., 15 pounds per month. So, Karl has lost a total of $15×5=75$ pounds over 5 months.

Karl’s weight today = k−75.

Given, their combined weight today is 450 pounds:

$$\begin{align*}s−25+k−75&=450\\ s+k&=550\end{align*}$$

From the problem, we know that Karl weighed the same as Scott does today 2 months ago. Thus, Karl’s weight 2 months ago was $k−3(15)=k−45$, because he loses 15 pounds each month.

$$\begin{align*}s−25&=k−45\\ s−k&=-20\end{align*}$$

Now, plugging (2) into (1):

$$\begin{align*}k-20+k&=550\\ 2k-20&=550\\ 2k&=570\\ k&=285\end{align*}$$ And from (2): $$\begin{align*}s&=550-285\\ s&=265\end{align*}$$

Basic Quadratics

If $y=x^2 +mx + 48$ has x-intercepts (a, 0) and (b, 0), where a and b are integers, what is the least possible value of m?

The correct answer is: D)

We know that ab=48 and a+b=m, so we just need to find all the possible combinations of a and b. We have the possible sets (1, 48), (2, 24), (3, 16), (4, 12), (6, 8), and their negative counterparts.

To find the value of m, we need to find the lowest sum of each pair of numbers.

It would be (-1, -48) whose sum is -49.

Functions & Symbols

For any two integers m and n, range(m, n) denotes the difference in the values of m and n. For example, range(3, 6) = 3. For the integers c and d, what is the value of range(c, d)?

(1) range(c, 6) = 20

(2) range(d, 15) = 5

A) Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.

B) Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are not sufficient.

The correct answer is: E)

(1) This statement allows for two possible values of c, 4 or 8 and provides no information about d; NOT sufficient.

(2) This statement allows for two possible values of d, 10 or 20 and provides no information about c; NOT sufficient.

(Together) There are still multiple possible differences for range(c, d); NOT sufficient.

The correct answer is E; both statements together are still not sufficient.

A rectangular tennis court is divided into six sections with a net splitting the court into two halves at the midpoint of its length. Each half has three equal sections consisting of a single large section and two equal smaller sections exactly half the size of the large section. If the length of the entire court is 24 meters, and the area of one of the smaller sections is 24 square meters, what is the width of the entire court?

A) 4 meters.

B) 6 meters.

C) 8 meters.

D) 12 meters.

E) 24 meters.

If the area of two smaller sections of one half of the court is equal to half of that half of the court’s area, then $24 = \frac{1}{2} × \frac{1}{2}lw$

Since the length of half of the court is 12 meters, solve for $w$ using the equation as $24 = \frac{1}{2} × \frac{1}{2}(12)w$

Multiply the full equation by 4 to find that $96 = 12w$ and divide by 12 to find that $8 = w$.

Rates and Work

Operating at the same time at their respective constant rates, Misha and Petro can repair 100 widgets in $q$ hours. Working by himself at his constant rate, Misha repairs 100 widgets in $w$ hours. In terms of $q$ and $w$, how many hours does it take Petro, working alone at his constant rate, to repair 100 widgets?

A) $\frac {qw}{w-q}$.

B) $\frac {qw}{q-w}$.

C) $\frac {q}{w+q}$.

D) $\frac {w}{w-q}$.

E) $\frac {q}{q-w}$.

Use the combined time formula where combined time = $\frac{time A × time B}{time A + time B}$, where time for Misha = $w$, combined time = $q$ and time for Petro = $x$.

Therefore, $ q = \frac{xw}{x + w}$.

Multiply the equation by $x + w$ to find $qx + qw = xw$.

Subtract by $qx$ and factor $x$ to find that $qw = x(w – q)$.

Divide by $w – q$ to find that $\frac{qw}{w – q} = x$.

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Free Practice for GMAT Quantitative Reasoning

the image is the cover for an article on gmat quantitative reasoning questions for consulting aptitude tests

Last Updated on January 16, 2024

The GMAT (Graduate Management Admission Test) is not only a valuable tool for those seeking to gain admission into top business schools but also serves as an effective resource for those preparing for consulting aptitude and recruitment tests, such as the BCG Online Case and Quantitative Reasoning Test, the Bain SOVA , the Kearney Recruitment Test , and others. This is particularly true for the GMAT’s Quantitative Reasoning section, which hones skills essential for acing consulting assessments.

Understanding the GMAT Quantitative Reasoning Section

Comprising 31 questions that must be answered within 62 minutes, the GMAT Quantitative Reasoning section measures analytical problem-solving abilities, with emphasis on basic arithmetic, algebra, geometry, word problems, and data analysis. It consists of two types of questions:

Problem-Solving (PS): These questions pose mathematical problems, presenting five possible solutions for choosing the correct answer. This section tests rudimentary quantitative skills, valuable in various consulting scenarios requiring quick, on-the-spot problem-solving.
Data Sufficiency (DS): Each question in this section presents a problem accompanied by two statements. Your task is to determine whether the information provided is sufficient to solve the problem. This section enhances your ability to analyze quantitative problems and identify necessary data, a skill that is critical in consulting roles and aptitude tests.

Problem-Solving questions present a mathematical problem that you’ll need to solve and choose the correct answer from five options. The problems can vary from relatively simple arithmetic to more complex concepts involving algebra, geometry, statistics, and combinations.

Let’s look at a sample PS question:

In this question, you’re asked to find the median of six consecutive numbers, given their sum. You would first find the average (sum divided by count: 111/6 = 18.5), and then since we know they are consecutive and an even set, the median would be between the third and fourth numbers – so, the average is also the median. The answer would be A. 18.5.

Data Sufficiency (DS)

Data Sufficiency questions present a statement followed by two pieces of data. Your job is to determine whether each piece of data is sufficient to answer the question when considered alone, or whether you need both, or whether you can’t answer the question even with both.

DS questions always have the same answer choices:

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D. EACH statement ALONE is sufficient E. Statements (1) and (2) TOGETHER are not sufficient

Here’s a sample DS question:

In this question, you’re asked to determine whether x is greater than y.

For Statement (1), if y = 1, then x = 1, and x is not greater than y. If y = 0, then x = -1, and x is less than y. So, statement (1) alone is not sufficient.

For Statement (2), if y = 0, we don’t know x’s value, so we can’t determine whether x > y. Thus, statement (2) alone is not sufficient.

Taken together, if y = 0 (from statement 2) and x = 2(0) – 1 = -1 (from statement 1), we can determine that x is not greater than y. So, the statements together are sufficient. The answer would be C.

Understanding the logic behind these types of questions is critical to achieving a high score in the Quantitative Reasoning section of the GMAT.

Why GMAT Quantitative Reasoning Practice Benefits Consulting Test Preparation

GMAT Quantitative Reasoning practice is beneficial in preparing for consulting aptitude and recruitment tests for several reasons:

Similar Skills Tested: Both the GMAT Quantitative section and consulting tests assess your analytical problem-solving skills, abilities to interpret data, and apply logic and reasoning—all crucial skills in the consulting field.
Time Management: Both tests are timed, so practicing under GMAT conditions can help enhance your speed and efficiency, crucial for consulting assessments.
Variety of Questions: The diversity of problem types in the GMAT’s Quantitative Reasoning section can broaden your problem-solving abilities, making you more adaptable to the array of questions posed in consulting tests.

Preparing for Consulting Aptitude Tests with GMAT Quantitative Reasoning

A solid preparation strategy includes understanding the format of the GMAT Quantitative section, reviewing basic mathematical concepts, and taking full-length practice tests under timed conditions. Practicing as much as possible can increase your speed and accuracy, which is key for performance on time-pressured consulting aptitude tests.

By making use of extensive resources, including hundreds of practice questions available online on platforms such as GMAT Club, Manhattan Prep, Magoosh, Kaplan, Veritas Prep, and Princeton Review, you can effectively prepare for consulting aptitude and recruitment tests like the BCG Online Case and Quantitative Reasoning Test or the Bain SOVA.

Key Topics Covered

The key topics covered in the Quantitative Reasoning section include, but are not limited to:

Word problems
Data analysis

It’s crucial to understand these topics deeply as they form the foundation of the questions asked in this section.

How to Prepare

Here are some general preparation strategies:

Understand the Format: Familiarize yourself with the structure of the test and the types of questions that will be asked. Practice is key here.
Review Basic Concepts: Make sure you understand basic arithmetic, algebra, and geometry.
Practice, Practice, Practice: Practice as much as possible to increase your speed and accuracy.
Take Mock Tests: Regularly take full-length tests under timed conditions to get a feel for the test environment.

Practice Questions

To help you get started with your preparation, we have compiled a list of resources that provide hundreds of practice questions.

GMAT Club : An extensive collection of Problem Solving and Data Sufficiency practice questions.
Manhattan Prep : Free GMAT practice test.
Magoosh : Large question bank with detailed answer explanations.
Kaplan : Offers a free GMAT practice test and questions.
Veritas Prep : Free GMAT practice test and question bank.
Princeton Review : Offers a free GMAT practice test.

You can also find 1000s of free quantitative reasoning questions on Google.

Please note: The websites linked above may require registration or sign-up to access the resources.

In conclusion, a robust preparation strategy for the GMAT Quantitative Reasoning section not only equips you with a high GMAT score but also primes you for success in consulting aptitude and recruitment tests. With consistent practice, you’ll enhance both your mathematical abilities and analytical problem-solving skills, opening doors to prestigious opportunities in the consulting field.

Practice with our dedicated resources.

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GMAT Sample Questions

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Want a preview of the question types you'll face on the GMAT? Try your hand at the GMAT practice questions below. Then, check your answers against our in-depth explanations to see how you did.

We pulled these GMAT sample questions from our book Cracking the GMAT and from our test prep course materials. For more GMAT practice, take a full-length practice test with us held under the same testing conditions as the real thing. Find out how you'd score, and get a personalized score report from us that shows your strengths and weaknesses.

GMAT Verbal Questions
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Essay Prompt

Below you'll find sample GMAT questions covering the three question types you'll encounter on the Verbal section: Sentence Correction , Critical Reasoning, and Reading Comprehension.

GMAT Sentence Correction Questions

1. In order to better differentiate its product from generic brands, the cereal company first hired a marketing firm that specializes in creating campaigns to build brand awareness and then retools its factory to produce a variety of different shapes of cereal. (A) then retools its factory to produce a variety of different shapes of cereal (B) retools its factory to produce a variety of different shapes of cereal (C) then retooled its factory to produce a variety of different shapes of cereal (D) then will retool its factory to produce a variety of different shapes of cereal (E) then produces a variety of different shapes of cereal through retooling its factory

Answer: (C) The actions of the cereal company are not in parallel form. First the company hired then it retools . Eliminate choice (A). Choice (B) still has the same error. Choice (D) changes the verb form incorrectly to the future tense. Choice (E) rewrites the sentence but retains the error.

[+] See the Answer

2. Believed to be one of the first widely read female authors of the Western world, Christine de Pizan's masterwork The Book of the City of the Ladies , was written in 1405 and is a history of the Western world from the woman's point-of-view. (A) Believed to be one of the first widely read female authors of the Western world (B) Written by one of the first widely read female authors of the Western world (C) One of the first widely read female authors of the Western world, as some believe (D) Written by what some believe as one of the first widely read female authors of the Western world (E) Believed by some as one of the first works by a widely read female author in the Western world

Answer: (B) As written, this sentence has a misplaced modifier error: the book, The Book of the City of the Ladies isn't believed by anyone to be an author— Christine de Pizan is. Choices (A) and (C) repeat that error and can be eliminated. Choices (B) and (D) both change the introductory phrase to clearly refer to a written work, but choice (D) uses the incorrect idiom believe as instead of the correct form, believe to be . Choice (E) repeats that idiom error.

GMAT Critical Reasoning Questions

1. One food writer wrote that reducing the amount of animal products in one's diet can contribute to better health and well-being. Based on this claim, some people are completely eliminating meat from their diets in order to be healthier. The argument above relies on which of the following assumptions?

Answer: (B) The argument states that some people are eliminating meat from their diets because reducing the amount of animal products in one's diet can lead to better health. Meat is only one type of animal product, however. The argument assumes that by eliminating meat, the people are reducing the total amount of animal products in their diets. Choice (A) addresses increasing the amount of vegetables and grains, but the argument just deals with animal products. Choice (B) correctly addresses the people who are eliminating meat and states that those people are not increasing their consumption of dairy, which is another instance of using animal products. Thus, these people are actually reducing the amount of animal products in their diets. Choice (C) addresses most food writers, who are irrelevant to this argument. Choice (D) addresses health lifestyles, which are irrelevant to this particular argument. Choice (E) addresses the reasons behind not eating animal products, which is irrelevant to the argument.

2. Studies reveal that a daily exercise regimen helps stroke survivors regain dexterity in their extremities. Being given an exercise routine and having a consultation with a doctor about the exercise routine have been shown to be effective mechanisms to get patients to exercise daily. From the above information, which of the following statements can be reasonably inferred? (A) A stroke survivor that is given a detailed exercise plan and consults her physician about the plan will regain full dexterity in her extremities. (B) If a stroke survivor is not given an exercise plan and does not consult with a doctor, she will not regain dexterity in her extremities. (C) Stroke survivors who are given an exercise routine and consult with a doctor about that routine will sometimes regain dexterity in their extremities. (D) Being given an exercise routine and having a consultation with a doctor about the routine is the best way to help a stroke survivor regain dexterity in their extremities. (E) Only being given an exercise routine is necessary to regenerate dexterity in the extremities of seniors who have suffered a stroke.

Answer: (C) This is an inference question, so evaluate the passage and then look for an answer choice that can be reasonably inferred from the information. The passage states that a daily exercise regimen helps stroke survivors regain dexterity in their extremities and that survivors who are given an exercise routine and who have a consultation with a doctor about the routine have been shown to be effective at getting patients to exercise daily . So it can be inferred that if a survivor is given a routine and consults with a doctor, they are more likely to exercise daily, which will help them regain dexterity. Choice (A) is an example of extreme language. The phrasing will regain full dexterity is not promised in the information in the passage, as the passage only states that a routine and consultations may help a survivor exercise more. Eliminate (A). Choice (B) is also an example of extreme language. There is no way to discern from the information provided that a strong survivor would not regain dexterity without an exercise routine and a consultation, so eliminate (B). Choice (C) is a reasonable inference to make from the information in the passage so keep (C). Choice (D) also contains the extreme language best way . The information does not compare this method with any other method so eliminate (D). Choice (E) is recycled language and does not address consulting with a doctor so eliminate (E). The correct answer is (C).

GMAT Reading Comprehension Questions

Although oft-maligned in modern culture, the pigeon once stood not only for speed and reliability but also for grace and beauty. Darwin himself became a pigeon fancier after beginning to work with the humble Columbia livia , discovering them to be more fascinating than he had formerly believed. During the Victorian age, in fact, raising show pigeons was a popular hobby, with new breeds continuously arising as amateur (and not-so-amateur) ornithologists crossed animals in the hopes of creating ever more fantastic creatures. One of the most sought-after varieties was known as the Almond Tumbler, a name presumably derived from the color of the birds combined with the distinctive flight style. Over the course of many generations, this bird was so manipulated as to have a beak so small as to prevent the adult birds from feeding their offspring. And yet, it was wildly popular, drawing high prices at auctions and high prizes at competitions. How then did an animal once so well-loved come to be so loathed? As recently as World War II, the military used pigeons to carry messages but today, many people would kick a pigeon before they would feed one. Perhaps it is just a problem of population density - a lack of esteem for that which is ubiquitous. Pigeons have become our constant urban companions and, as such, have been transformed from symbols of peace, plenty, and prosperity, to representatives of disease and decay.

1. The primary purpose of this passage is to (A) convince the reader of the nobility of the pigeon, based on its history as a symbol of virtue (B) dissuade the reader from mistreating a once-majestic animal that has fallen from favor (C) rebut claims that the pigeon carries disease any more frequently than do other domestic animals (D) promote a renewal of pigeon fancying and a resurgence of breeds such as the Almond Tumbler (E) suggest that there might be more to the story of some urban wildlife than is commonly known

Answer: (E) The passage gives a brief description of the pigeon's place in recent human history and then goes on to contrast that with modern perspectives of the birds. Choice (A) goes too far—the author doesn't give any indication of believing the pigeon to be noble. Choice (B) focuses too specifically on a side comment in the second paragraph. Choice (C) also focuses too specifically on a side comments—the passage is not primarily about disease. Choice (D) is too strong—the passage isn't really promoting any specific action. Choice (E) remains neutral and informational, as does the passage.

2. The case of the Almond Tumbler is most analogous to which of the following? (A) a strain of wheat that can be grown in plentiful quantities but loses much of its nutritional value in the process (B) Arabian horses that are able to run at phenomenal speeds due to centuries of careful breeding designed to enhance those physical attributes (C) vitamins that were purported to provide all of the necessary nutrients but have since been found not to be very effective (D) the dachshund, a popular breed of dog that is nonetheless prone to severe back problems, due to weaknesses exacerbated by targeted breeding (E) the wild rock doves that are most commonly found nesting in the faces of cliffs far from human habitation

Answer: (D) The Almond Tumbler is described as a breed of pigeon that was very popular during the Victorian era. The passage also mentions that the selective breeding used to create that particular kind of bird also led to tiny beaks that kept parent birds from feeding their babies. Therefore, the best analogy would be another animal that is popular even though it has problems due to its design. Choice (A) is incorrect because it leaves out the aspect of popularity. Choice (B) is only positive and you need something that's also negative. Choice (C) is not about something that has been bred for a specific purpose, nor does it deal with popularity. Choice (D) correctly refers to a popular animal with a common health problem. Choice (E) does not refer to pigeons that have been bred by humans.

3. The passage suggests that (A) pigeons were once known for flying with celerity (B) the Almond Tumbler was the most beautiful breed of pigeon (C) Darwin was infatuated with his fancy pigeons (D) modern pigeons are dirtier than the fancy pigeons of yore (E) only scientists should breed new kinds of animals

Answer: (A) For a question this open-ended, it's usually best to check each of the answers against the passage. Choice (A) appears to match the opening line of the passage, which states that the pigeon once stood not only for speed and reliability. Choice (B) goes too far—although many Victorians seems to have loved the Tumbler, there's no evidence that it was definitively the most beautiful. Choice (C) also goes too far—the passage mentions that Darwin was fascinated by his pigeons, not that he was infatuated. Choice (D) draws an incorrect assumption—the passage comments that the common opinion has changed, not the pigeon itself. Choice (E) is not supported by the passage, which states that amateurs, as well as trained individuals, bred pigeons.

Below you'll find GMAT sample questions covering the two question types you'll encounter on the Quantitative section: Problem Solving and Data Sufficiency.

Problem Solving Questions

1. A certain company sells tea in loose leaf and bagged form, and in five flavors: Darjeeling, earl grey, chamomile, peppermint, and orange pekoe. The company packages the tea in boxes that contain either 8 ounces of tea of the same flavor and the same form, or 8 ounces of tea of 4 different flavors and the same form. If the order in which the flavors are packed does not matter, how many different types of packages are possible? (A) 12 (B) 15 (C) 20 (D) 25 (E) 30

Answer: (C) Begin by figuring out how many different ways you can package the tea in boxes that contains 8 ounces of tea, all of the same flavor. There are five flavors, each flavor can come in either loose leaf or bagged form, so 5 flavors x 2 forms = 10 different ways to package the tea in boxes that contain only one flavor each. Now find the number of different ways to package 4 different flavors of the same form per box. In this case, you must choose 4 of 5 possible flavors, and order does not matter, so the formula is 5 x 4 x 3 x 2 ⁄ 4 x 3 x 2 x 1 = 5 different ways to combine the 4 flavors. Each combination can come in either loose leaf for bagged form, so you have 2 different forms x 5 different combinations = 10 total possible ways to combine the 4 flavors in either bagged or loose-leaf form. Thus, the total number of combinations is 10 + 10 = 20 total combinations. The answer is choice (C).

2. Karen sold her house at a loss of 25 percent of the price that she originally paid for the house, and then bought another house at a price of 30 percent less than the price she originally paid for her first house. If she sold the first house for $225,000, what was her net gain, in dollars, for the two transactions? (A) $15,000 (B) $25,000 (C) $60,000 (D) $75,000 (E) $90,000

Answer: (A) If Karen sold her first house for $225,000 and at a loss of 25 percent, then 25 percent of the original price equals $225,000. 75 ⁄ 100 x = 225,000, so x, or the price she originally paid, equals $300,000. Thus, Karen lost $75,000 on the sale of her first house. If she bought a second house for a price of 30 percent less than $300,000, then the second house cost $210,000, so she gained $90,0000. $90,000 - $75,000 = $15,000, so the answer is choice (A).

Sample Data Sufficiency Questions

1. In a certain company, at least 200 people own manual transmission vehicles. If 12 percent of the people who own manual transmission vehicles also own automatic transmission vehicles, do more people own automatic transmission vehicles than own manual transmission vehicles? (1) 5 percent of the people who own an automatic transmissions vehicle also own a manual transmission vehicle. (2) 15 people own both an automatic transmission vehicle and a manual transmission vehicle. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (D) EACH Statement ALONE is sufficient. (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Answer: (A) According to statement (1), 5 percent of the people who own an automatic transmission vehicle also own a manual transmission vehicle. The question also indicates that 12 percent of the people who own a manual transmission vehicle also own an automatic transmission vehicle. Both figures relate to the total number who own both, so that means that 5 percent of the automatic transmission owners = 12 percent of the manual transmission owners. The overlap in ownership makes up a smaller percent of those who own automatic transmission vehicles, so there must be more people who own automatic transmission vehicles. Statement (1) is sufficient, so you can eliminate choices (B), (C), and (E). Statement (2) indicates that 15 people own both an automatic transmission vehicle and a manual transmission vehicle, so you know that 12 percent of the people who own a manual transmission is equal to 15 people. 12 ⁄ 100 = 15, so x = 125. Thus, there are 125 people who own a manual transmission vehicle. However, you have no further information to allow you to calculate the number of people who own automatic transmission vehicles, so statement (2) is insufficient. The answer is choice (A).

2. What is the value of x ⁄ 2 ? (1) x is 1 ⁄ 5 less than 9 ⁄ 10 (2) x is between 2 ⁄ 5 and 4 ⁄ 5 (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (D) EACH Statement ALONE is sufficient. (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Answer: (A) Statement (1) allows you to find the value of x, so you can answer the question. (If x is 1 ⁄ 5 less than 9 ⁄ 10 , then 9 ⁄ 10 - 1 ⁄ 5 = x. 1 ⁄ 5 = 2 ⁄ 10 , so x equals 9 ⁄ 10 - 2 ⁄ 10 = 7 ⁄ 10 . If x equals 7 ⁄ 10 , then x ⁄ 2 = 7 ⁄ 10 divided by 2, or 7 ⁄ 20 .) Statement (1) is sufficient, so eliminate choices (B), (C), and (E). According to statement (2), x is between 2 ⁄ 5 and 4 ⁄ 5 . That means that one possible value for x is 3 ⁄ 5 , but another possible value is 7 ⁄ 10 . Statement (2) is insufficient, so the answer is choice (A).

Below you'll find examples of how you'll be asked to use a chart, graph, or table to answer questions on the Integrated Reasoning section.

Sample Integrated Reasoning Questions

Item 1: Andre is buying gifts for his office staff. He wants to spend exactly $280 and he can buy either sweatshirts, which cost $22, or baseball caps, which cost $26. In the table below, choose the number of sweatshirts and the number of baseball caps that Andre should buy.

Answer: Sweatshirts, 8; Baseball caps 4 To solve this question, systematically test out the answer choices. The equation you need to solve is 22s + 26h = 280, in which both s and h are integers and s represents the number of sweatshirts and h represents the number of baseball caps. So, start with plugging in 4 for sweatshirts and see if the number of baseball caps is an integer. 22(4) +26h = 280 h = 7.38 Since the number of baseball caps is not an integer, Andre could not have bought 4 sweatshirts. Keep trying more sweatshirts one by one until you find an answer that will you an integer value for baseball caps. 8 sweatshirts will give you 4 baseball caps.

Question 2-1 The ratio of the U.S. population in 2000 to the U.S. population in 1900 is closest to __. (A) 1 to 4 (B) 2 to 7 (C) 2 to 1 (D) 3 to 1 (E) 11 to 3

Answer: (E, 11 to 3) According to the graph, the U.S. population in 2000 was a little bit more than 275 million, and the U.S. population in 1900 was a little over 75 million. Since the question asks what the ratio is "closest to," these numbers are good enough to approximate. 275 to 75 can be reduced by 5 to get 55 to 15, which can be reduced by 5 again to get 11 to 3. Alternatively, you could reduce 275 to 75 by 25 to get this same ratio.

Question 2-2 The U.S. population in 1950 was approximately __ of the U.S. population in 1850. (A) 800% (B) 600% (C) 200% (D) 85% (E) 15%

Answer: (B, 600%) The question asks what percent the U.S. population in 1950 is of the U.S. population in 1850. To get this you need to calculate population 1950 ⁄ population 1850 x 100. Since the U.S. population in 1950 is higher, you want something that is greater than 100%. Eliminate 85% and 15%. Since the sentence says "approximate" and also since the remaining answer choices are not close to each other, you can estimate the values. According to the chart, the population in 1950 was about 150 million and the population in 1850 was about 25 million. Therefore, you need to calculate 150 ⁄ 25 x 100 = 6 x 100 = 600%.

Question 2-3 The U.S. population increased by approximately __ from 1900 to 1950. (A) 25% (B) 33% (C) 50% (D) 100% (E) 200%

Answer: (D, 100%) To get percent increase, you need to use the formula difference ⁄ original x 100. The population in 1900 was about 75 million, and the population in 1950 was about 150 million. The difference between the two figures is 75 million. Therefore, the percent increase is 75 ⁄ 75 x 100 = 100%.

Below you'll find a sample Analytical Writing Assessment (AWA) question. On the GMAT you'll have 30 minutes to write a critique of the argument.

Analysis of an Argument

The following appeared as part of a medical advertisement in a magazine.

A new medical test that allows the early detection of a particular disease will prevent the deaths of people all over the world who would otherwise die from the disease. The test has been extremely effective in allowing doctors to diagnose the disease six months to a year before it would have been spotted by conventional means.

Discuss how logically convincing you find this argument. In explaining your point of view, be sure to evaluate the line of reasoning and the use of evidence in the argument. For example, it may be necessary to consider what questionable assumptions underlie the thinking and what other explanations or counterexamples might weaken the arguments conclusion. You can also discuss what kind of evidence would strengthen or refute the argument, what changes in the argument would make it more logically persuasive, and what, if anything, would enable you to better evaluate its conclusion.

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