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Free GMAT Practice Questions

Practice makes perfect—or at least that's how the old saying goes—and it certainly applies to our free GMAT practice questions. Our Free Practice Questions are designed to give you the thorough understanding of how to go about solving a problem that you crave. Our thorough explanations show you what to expect from each GMAT question, detailing question-specific hurdles and common traps. Thankfully, our practice questions provide a wide variety of question types spanning across all sections, securing an abundance of insight-turned-strategy you can implement on test day to turn into high-scoring gold.

Manhattan Review prides itself in providing quality free practice questions to all prospective students, so please take a crack at the 52 free questions we have to offer as a courtesy to all GMAT learners. In the end, the only way to find out where you need your score to be is to discover where it currently is. Take advantage of this free resource that's sure to help you along your way to a high score.

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Problem Solving Practice Test 1

The GMAT Problem Solving questions will test your ability to evaluate information and solve numerical problems. Our practice problems are designed to be very challenging in order to prepare you for the harder-level questions found on the GMAT. Answers and detailed explanations are include with each problem. Start your test prep now with our free GMAT Problem Solving practice test.

Directions: Solve the problem and select the best of the answer choices given.

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GMAT Prep Online Guides and Tips

10 top tips for gmat problem solving questions.

problem solving gmat practice questions

For many test takers, the quantitative section of the GMAT is particularly daunting. The challenging section includes two types of questions: data sufficiency and problem solving. While data sufficiency questions are undoubtedly the more notorious question type, GMAT problem solving questions can also be quite tricky.

In this guide, I’ll give you an in-depth look at GMAT problem solving questions. First, I’ll cover what they are and what types of math they cover. Then, I’ll give you the top 10 tips for acing GMAT problem solving questions. Finally, I’ll walk you through solving five sample problem solving questions spanning a variety of topics.

What Are GMAT Problem Solving Questions?

Problem solving GMAT questions assess how well you can solve numerical problems, interpret graphs and tables, and evaluate information. In plainer language, problem solving GMAT questions are the “traditional” math question type that you’ll see on the GMAT quant section.

While there isn’t a set number of problem solving questions that you’ll see on the GMAT, you can bet that the quant section will be divided just about 50/50 between problem solving and data sufficiency questions. There are 31 total questions on the GMAT quant section, so you there will be either 15 or 16 problem solving questions on the GMAT quant section.

Problem solving questions look a lot like the math questions you’ve seen on other tests. GMAT problem solving questions are all multiple choice questions, with five different answers. Depending on the content tested, problem solving questions may be presented as an equation, a word problem, a diagram, a table, or a graph.

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Contrary to popular belief, the GMAT quant section doesn’t test on advanced math concepts. The quant section tests your content and analytical knowledge of basic math concepts, such as arithmetic, algebra, and geometry. The same holds true for GMAT problem solving questions – you’ll be asked to apply your knowledge of high school math concepts to questions that are presented in a more challenging and analytical way. For more information about the concepts covered on the GMAT quant section, check out our guide to GMAT quant .

GMAT problem solving questions only test high school math concepts.

10 Tips for Mastering GMAT Problem Solving Questions

Here are the top tips that you can use to master GMAT problem solving questions.

#1: Master the Fundamentals

GMAT problem solving questions only test high school math concepts. In many ways, this is good news. You’ll have likely encountered every type of math you’ll see on the GMAT before you start studying. Just because the math on the GMAT is relatively basic, however, doesn’t mean that it’s not tricky.

The GMAT tests basic math concepts in complicated ways. Problem solving GMAT questions often ask you to use more than one skill at one time, so you need to have strong mastery of many different concepts.

The key to GMAT problem solving mastery, then, lies in mastering the fundamentals.  Memorize the exponent rules. Memorize common roots and higher powers. Memorize the formulas for finding area of different shapes. Know how to find mean, median, mode, and standard deviation without blinking an eye. Thoroughly understanding the material covered on the GMAT will save you time and boost your score on test day.

#2: Practice Doing Calculations Without a Calculator

As I mentioned, you won’t be able to use a calculator on the GMAT. As such, y ou should prepare for problem solving GMAT questions without using a calculator to ensure that you’re used to making basic calculations by hand.

Get used to using scratch paper for calculations and double-checking your work to make sure there are no errors. In particular, make sure that you spend time practicing multiplying and dividing fractions and decimals without a calculator, as you’ll have to do both on the GMAT. The more non-calculator practice you get in before test day, the better prepared and more comfortable you’ll be.

You won't be able to bring a calculator to use on the GMAT, so practice without one!

#3: Use High-Quality Practice Materials

The best way to prepare for the GMAT is by using real GMAT problem solving questions to practice, since they’re the only questions that simulate the GMAT’s style and content with 100% accuracy.  The problem-solving questions have a unique style and logic that many unofficial resources struggle to replicate. Fortunately, there are a ton of real GMAT questions available , and some are even free !

You’ll likely want to supplement each of these resources with other third party tools to help you study. Make sure that any books or online materials you’re using are accurate, useful, and well-respected. A good way to check about the reliability of a book or resource is to read reviews of the resource on Amazon or forums like Beat the GMAT or GMAT Club. We’ve also reviewed the best GMAT books and the best GMAT online resources (coming soon) for you.

#4: Plug In Numbers

You can solve many GMAT problem solving questions by plugging in real numbers for the variables in equations.  Look for questions that have algebraic answers, or questions that ask for the values of algebraic expressions instead of just the values of variables when plugging in numbers. For instance, consider the following question.

If x < y < 0, which of the following is greatest in value?

e. 2y – x

For this question, you can pick real numbers that fit the parameters of the question (such as y = -2 and x = -3), and then plug them into each answer to see which answer has the greatest value.

Here are a few tips for plugging in numbers. First, try to use easy, whole integers that fit the constraints of the question. Second, if the question is asking you to determine a value, you can use the numbers yo’ve plugged in to find the matching answer. If the answers are also algebraic terms, keep plugging in your numbers until you get a match. Third, be careful when you’re plugging in numbers! Make sure you go through every one of the answers, as you may find two answers that match with the numbers you’ve chosen. If that’s the case, try plugging in new numbers or solving the problem in a different way, until you’ve only gotten one correct answer.

The writers of the GMAT know that people generally pick positive, whole numbers to plug into their equations. Don’t forget about negative integers, positive and negative fractions, positive and negative decimals, etc., when plugging in numbers to solve a question.

#5: Work Backwards Using Answer Choices

The GMAT normally arranges answer choices in the ascending numerical value on the quant section. Consider the following example, which we’ll go into more depth on in the next section.

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When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000 dollars. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?

Notice how the answer choices are written in ascending numerical value. This arrangement means that you can try to plug in an answer and work backwards if you’ve got no idea where to start on a particular question. I’d suggest plugging in the middle answer, so that way you’ll know whether you need to go higher or lower with your answer. You can also use this method to decide which answers to try to plug in next, as well as automatically eliminate the other answers.

#6: Don’t Rely on Your Eyes

When tackling geometry questions, don’t rely on your eyes to estimate angle sizes, lengths, or areas of figures. Instead, use the numbers provided and your own mastery of geometry concepts. Geometry figures aren’t always drawn to scale, and assuming they are can get you into trouble.

You’ll never encounter a GMAT quant question that you can answer simply by visual estimation. GMAT problem solving questions are designed so that you have to use the information in the question, as well as any information in the diagrams, graphs, charts, or tables, to help you solve the question. That means that you won’t be able to see a triangle and estimate the length of one of its sides just by looking at it. You’ll need to use the information in the question to help you

#7: Remember That the Numbers Will Work Out

The writers of the GMAT know that you’re not allowed to use a calculator on the quant section. That means that you’ll be able to solve every question using your mastery of fundamental math concepts, a pencil, and scratch paper. If you’re working yourself into a quagmire of exceedingly complicated calculations, stop, take a breath, and reassess the question. You’re likely over-thinking something.

#8: Use What You Know

No matter how difficult the question may look, remember that you’ll only need to use high school level math to answer it. Start small on questions by using what you know. If you break the problem down to small steps, beginning with what you know, you’ll be able to work towards an answer.

Consider the following sample diagram, which I’ll go into more depth about in the next section.

Screen Shot 2017-04-23 at 8.05.49 AM

When you’re approaching GMAT problem solving questions, make sure you’re using all the information in the question and any corresponding charts, tables, or diagrams to find your answer.

#9: Practice Your Timing

One of the keys to success on the GMAT quant section is being able to quickly solve complex math problems.  If you can solve most problem solving questions in a minute or less, you’ll have plenty of time leftover to spend on more difficult questions.

To improve your timing, practice with a timer when you’re working on practice sets. Give yourself two minutes to solve every question in your practice set, and see how that feels. Slowly decrease the amount of time you’re giving yourself, until you’re averaging one minute on most questions.

Time yourself to see how quickly you can solve questions.

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#10: Use Flashcards to Help You Memorize Important Formulas

As I mentioned in previous tips, you won’t get to use a formula cheat sheet on the GMAT. You’ll have memorize all the formulas you expect to need on test day. You should spend time before test day memorizing the formulas that you’ll see on the GMAT.

Using flashcards is a great way to build your knowledge so that you can quickly recall and use important formulas on test day. Flashcards help you learn to quickly and accurately remember information by forcing you to focus on one small piece of information at a time. Flashcards are also highly portable, and easy to carry with you so that you can practice when you have downtime, such as on your commute to and from work or school. There are many free GMAT flashcard resources out there, but it’s always best to make your own flashcards. In our guide to the best GMAT flashcards , we review the best GMAT flashcard resources out there, as well as tell you the best way to study using flashcards.

5 Sample Problem Solving GMAT Questions

These five samples questions will help you see the types of concepts covered in GMAT problem solving questions. Please note: there’s a lot of content covered in GMAT problem solving questions. While I picked sample questions that represent a wide range of topics covered by GMAT problem solving questions, there are many more content areas that you’ll see on the test.

Problem Solving Sample Question #1

We know that Leo paid $87.50 of import tax on the total value of an item in excess of $1,000.

Let’s start by saying that x stands for the total value of the item. We also know that x ≥ 1000, because Leo had to pay import tax on the part that was in excess of $1,000.

So, (x – 1000) can represent the part that Leo had to pay the 0.7% import tax on.

We can therefore write the equation:

0.7(x – 1000) = 87.50

Multiply both sides by 0.7 to isolate x, which yields us:

X – 1000 = 1250

Add 1000 to both sides to isolate x which yields us:

X = 1250 + 1000

The correct answer is C. You could also get the right answer by plugging in the different values. As I mentioned in the tips section, start with the middle number. In this case, plugging in C would yield you the correct answer. However, if it didn’t, you’d be able to use that information to eliminate other answers and decide what to plug in next, as discussed in the earlier tip.

Check out our guide to GMAT rate problems to learn more about how to solve interest rate questions.

Problem Solving Sample Question #2

If the average (arithmetic mean) of the four numbers 3, 15, 23, and (N+1) is 18, then N =

This question requires us to understand how to find the arithmetic mean. You find the arithmetic mean of a set of values by dividing the sum of all the values by the total number of values. So, in this case, that yields us the following equation:

3 + 15 + 32 + (n + 1)/4 = 18

3 + 15 + 32 + (n+1) represents the sum of all the values.

4 represents the total number of values.

Now, let’s simplify this equation. In order to isolate n, let’s first multiply each side by 4, which yields us the new equation:

3 + 15 + 32 + (n +1) = 72

We can simplify that equation to get:

51 + N = 72.

Then we can solve for n by subtracting 51 from both sides.

N = 72 – 51

The correct answer is C.

Problem Solving Sample Question #3

Screen Shot 2017-04-23 at 8.04.15 AM

This question is all about interpreting graphs. The question asks us to determine the difference between the highest and lowest tides.

First, let’s start off by determining the highest tide. The highest tide seems to be at 11:30 a.m., which is 2.2 ft.

The lowest tide is 0.5 feet below the baseline, which occurs at 6 pm.

Therefore, the equation to express the difference between the heights is [2.2 – (-0.5)] = 2.7 ft.

The correct answer is E.


Problem Solving Sample Question #4

A flat patio was built alongside a house as shown in the figure above. If all angles are right angles, what is the area of the patio in square feet?

You calculate the area of a rectangle by multiplying length x width. 35 x 40 = 1400 ft.

Screen Shot 2017-04-23 at 8.05.41 AM

Now, because the patio is missing a portion where it intersects with the house, we have to find the area of that missing portion. From the diagram, we can see that the part where the patio intersects with the house is a square with the dimensions 20 ft by 20 ft.

We can find the area of that square by multiplying length times width, so 20 x 20 = 400 ft.

Now to find the area of the patio, we simply subtract 1400 – 400 = 1000 ft.

The patio has an area of 1000 square feet.

Problem Solving Sample Question #5

Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?

Let’s start off by defining what we know.

We know that Mark sold 10 less boxes than n. We can express the number of boxes that Mark sold as n – 10.

We know that Ann sold 2 less boxes than n. We can express the number of boxes that Ann sold as n – 2.

We also know that they each sold at least one box of cookies. Thus, we can say that n – 10 ≥ 1 and n – 2 ≥ 1.

Thus, we know that n ≥ 11, because we need at least 11 boxes to make Mark’s statement (n – 10 ≥ 1) true.

We also know that they sold less than n boxes. We can express this as:

(n – 10) + (n – 2) < n. If we solve through for n in this equation, we get that n < 12.

We therefore know that n ≥ 11 and n < 12, which tells us that n = 11.

The correct answer is A.

Review: How to Attack Problem Solving GMAT Questions

GMAT problem solving questions are more traditional than data sufficiency questions. You’ll see concepts presented in a straightforward way that is very similar to how you’ve seen math questions posed on other standardized tests.

But that doesn’t mean these questions are easy or simple! Problem solving questions cover a wide range of math concepts, from algebra to geometry to number properties and more. Work on mastering fundamental math concepts so that you can work quickly and successfully through problem solving questions on test day.

What’s Next?

There’s a lot of content covered on the GMAT quant section, so if you’re looking for specific tips on tackling a part content area check out some of our other guides (such as our guides to GMAT percents , probability , and geometry ). These guides will help you build up the fundamental knowledge you need to succeed on the GMAT.

Feel like you’ve gotten the hang of GMAT problem solving questions, but wondering what’s up with the other half of the GMAT quant section? Data sufficiency questions are undoubtedly a bit strange, and very different stylistically from any traditional math question you’ve encountered on other standardized tests. Check out our guide to data sufficiency questions  to learn more about this unique question type and how to master it.

Wondering how to build in practice on problem solving questions to your GMAT studying? Look no further than our comprehensive GMAT study plan article . In this guide, you’ll find four different GMAT study plans designed to maximize your time and boost your score. You’ll learn how much time you should devote to each section of the test and get recommendations on resources you can use to supplement your practice.

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Problem-solving questions are standard multiple-choice questions with five answer choices: A, B, C, D, and E. These problems test your basic math skills, your ability to apply elementary math concepts, and your ability to reason quantitatively.

Problem-solving questions cover three subject areas: arithmetic, elementary algebra, and geometry. The number of questions for each of these three subjects is in the neighborhood of

  • Arithmetic: 13
  • Elementary algebra: 6
  • Geometry: 3

When working on a problem-solving question, make sure that you read the question carefully, know exactly what you have to find, solve the problem, and select the best of the answer choices given.

Remember: All numbers in the quantitative section are real numbers, and all figures shown are drawn as accurately as possible, unless stated otherwise. Straight lines may sometimes appear jagged on the computer screen.

When working on the quantitative section of the GMAT, keep in mind the following:

  • It is important to pace yourself. You have 75 minutes to do 37 questions, which is approximately 2 minutes per question.
  • You may not skip over a question. The computer will not present the next question until you've answered the current one on the screen.
  • Make an educated guess if you aren't sure about the answer. There is a penalty for wrong answers, but there is also a penalty for unanswered questions, so if you're struggling with a particular question, you're better off making an educated guess and moving on.
  • Calculators are not allowed.

Sample practice question: Arithmetic

There are 200 marbles in a box. All the marbles are either red or blue. If there are 40 more red marbles than blue, how many red marbles are there in the box?

The correct answer is C. Let x be the number of blue marbles, and x + 40 be the number of red marbles. There are 200 marbles in the box, so you have x + x + 40 = 200, which is equivalent to 2x + 40 = 200, or x = 80. Thus, the number of red marbles is x + 40 = 120.

Sample practice question: Algebra

Three times a number is the same as the number added to 60. What is the number?

The correct answer is C. Let x be the number. Then, you have 3x = 60 + x, which is equivalent to 2x = 60, or x = 30. The number is 30.

Sample practice question: Geometry

If the length, width, and height of a rectangular box measure 1, 3, and 8, respectively, what is the total surface area of the box?

The correct answer is C. A rectangular box has six faces. The top and bottom faces both have surface areas (8)(3) = 24 for a total of 2(24) = 48. The front and back faces both have surface area (8)(1) = 8, for a total of (2)(8) = 16. The left and right faces both have surface area (3)(1) = 3 for a total of (2)(3) = 6. The surface area of the box is 48 + 16 + 6 = 70.

Find the discriminant value for the following equation.

x 2 + 5 x – 6 = 0

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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.

problem solving gmat practice questions

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?

Articulate the variables as, s = Scott’s weight 5 months ago and k = Karl’s weight 5 months ago.

Scott’s weight loss rate is given as 5 pounds per month, and hence he has lost a total of \(5×5=25\) pounds over 5 months.

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.

Plane Geometry

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 \(8 = w\).

3D Geometry

A cube dropped into a cylindrical bucket raises the height of the water in the bucket from 50 percent of the height of the bucket to 75 percent of its height. If an edge of the cube is equal to half of the height of the bucket, what is the ratio of the volume of the cube to the volume of the bucket?

A) \(\frac{1}{6}\)

B) \(\frac{1}{4}\)

C) \(\frac{1}{3}\)

D) \(\frac{1}{2}\)

E) \(\frac{3}{4}\)

The correct answer is: B)

Recognize that the exact dimensions of the bucket and cube are irrelevant. If the height of the water in the bucket increases from 50 percent to 75 percent, then the cube is now occupying 25 percent or \( \frac{1}{4}\) of the bucket’s volume.

Coordinate Geometry

If line \(d\) in the coordinate plane has the equation \(y = mx + b\), where \(m\) and \(b\) are constants, what is the slope of line \(d\)?

(1) Line \(d\) intersects the line with equation \(y = 6x + 2\) at the point (1, 8).

(2) Line \(d\) is parallel to the line with equation \(y = (2 – m)x + b – 4\).

Note that the slope of a line with equation \(y = mx + b\) is\( m\).

(1) A line passing through the point (1, 8) can have any value for its slope, so it is impossible to determine the slope of line \(d\).

For example, the line \(y = x + 7\) intersects \(y = 6x + 2\) at (1, 8) with a slope of 1, while the line \(y = 2x + 6\) intersects \(y = 6x + 2\) at (1, 8) with a slope of 2; NOT sufficient.

(2) Parallel lines have the same slope, and it is possible to solve for the slope as \(m = 2 – m\), \(2m = 2\), and \(m = 1\); SUFFICIENT.

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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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. 

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

GMAT Problem Solving, Sample Question #1

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

GMAT Problem Solving, Sample Question #2

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

Sample GMAT Questions by Topic

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