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# GRE Quant Practice Questions

Your GRE Quant Preparation would experience a boost by practising GRE Quant Questions regularly. This would improve your chances of securing a higher score and thus get admission calls from leading graduate schools. By solving some of these sample questions, you will get a taste of what to expect on the day of the examination.

The best GRE quant practice questions must fulfil the following criteria

• They should be organized by difficulty level
• They should test you in the same way a real GRE quant question would
• They must resemble real questions in formatting and style

In this section, you will find the different types of GRE questions to expect according to their difficulty levels. We have provided answers to every question. A detailed explanation about the steps to resolve the question has also been offered for each answer.

## There are 12 questions in all. We hope you would enjoy solving these:

GRE quantitative section in the GRE General test comprises the following four types of questions:

1. Quantitative comparison questions
2. Multiple-choices Questions — Select any One Answer Choice
3. Multiple-choices Questions — Select One or More than One Answer Choice
4. Numeric Entry Questions

These questions are either presented independently or as a part of a data interpretation set.

For making it easier to navigate, we have provided this handy table which will enable you to get redirected to the question of your choice:

Type of question Quantitative comparison Multiple choice (Select any one answer choice) Multiple choice (Select one or more than one answer choice) Numeric Entry
Simple 1 4 7 10
Average 2 5 8 11
Challenging 3 6 9 12

Let us take a look at a solved sample for each type to get a better understanding of what you are up against!

## Quantitative Comparison Questions

Every quantitative question will have a variation of the following options

1. Quantity A is greater
2. Quantity B is greater
3. The two quantities are equal
4. The information provided is insufficient.

It is clear that the first three options require you to compare two quantities. Either one of them is greater than the other or both are equal. However, check out the last option – ‘The information provided is insufficient’. You should never be hasty in choosing this.

Quantitative comparison questions account for almost 35% of the GRE Quantitative Reasoning section. Therefore a good score in this section is likely to improve your overall score. You shouldn’t take more than a minute to solve each problem.

Here are some important tips:

• Focus on comparing the two quantities rather than being fixated on calculations.
• Insert numbers whenever algebraic expressions are used.
• Work towards simplifying the relationship

Here are some GRE quant practice questions to illustrate quantitative comparison questions:

Difficulty level: Simple

The profit gnerated by company ABC is divided between its two founders Jack and Mark in a 4:3 ratio respectively.

Column 1 Column 2
Jack’s share when the profit generated by company ABC is \$ 8000 \$5000

1. Quantity in column 1 is higher
2. Quantity in column 2 is higher
3. The data provided isn’t enough to determine the answer
4. Both the quantities given are equal

Solution

Here is how you solve this question:
The ratio of profit between Jack and Mark is 4:3. The total profit generated is \$ 8000.
Since the units of the antecedent (4) and consequent (3) are the same, we can concur that 4x+3x = 8000. Therefore, x = 8000/7 = 1142.857
Therefore 4x = 4571.428 and 3x = 3428.571
Hence, the profit earned by Jack is \$ 4571.428 and Mark is \$ 3428.571. Therefore Jack’s share is \$ 4571.428 when profit earned by the company is \$ 8000. But value in column 2 is \$ 5000.
Therefore Jack’s share is less than \$ 5000.
Hence the correct answer is option b

1. Quantity in column 1 is higher
2. Quantity in column 2 is higher
3. The data provided isn’t enough to determine the answer
4. Both the quantities given are equal

Solution

This question becomes convenient to solve if you can visualise and draw the given condition. First, you must draw a circle. Then sketch out a square by ensuring one of the sides of the square is the diameter of the circle.

This should be drawn in such a way, that if the circle is moved into the square, it will fit in the square:

You can see that once the circle moves inside the square there are portions of the square which aren’t occupied by the circle. From the diagram itself, one can infer that the area of the square is greater than the area of the circle.

For those, who find it easier to remember formulas, the following solution can be used:

Area of a circle is πr^2. Area of a square is 4r^2The value of pi (π) is 3.14. Therefore, 4r^2 is greater than πr^2. Hence the area of the square is greater than the area of the circle. Hence the correct answer is option b)

Difficulty level: Challenging

Assume that y is greater than 3.
Quantity 1: (4y+2)/5
Quantity 2: Y

1. Quantity in column 1 is higher
2. Quantity in column 2 is higher
3. The data provided isn’t enough to determine the answer
4. Both the quantities given are equal

Solution

Step 1 -> Multiply left hand side and right hand side by 5. Then you will get (4y+2) on the left hand side and 5 y on the right hand side. So your equation becomes 4y+2 = 5y
Step 2 -> Now subtract 4y from both sides. So the equation becomes 2 = y
Now this equation has been simplified. Compare 2 and y. If you recall, it was mentioned at the beginning that y is greater than 3. Therefore, 2 is less than y.
But the question is not about the relationship between 2 and y. It is about the relationship between the left hand side quantity and the right hand side quantity.
However, since we have established that 2 is less than (<) y, you just need to keep reversing the steps.
Reverse step 2 by adding 4 y to both sides. Therefore you will get 2+4y < y+4y = 2+4y < 5y
Reverse step 1 by dividing both sides by 5. Thus you will get (2+4y)/5 < (5y/5) = (4y+2)/5 < y. Therefore the answer is b

## Multiple-choice Questions — Select One Answer Choice

A multiple choice question would have five answer options. But only one of them would be the correct answer.

Here are some handy tips to deal with MCQ – Select one answer choice

• Use the process of elimination. You will be able to improve your chances of selecting the correct answer.
• Guesstimate. For certain questions, you would not need to spend a lot of time in calculations. You can skim through the options to approximate the correct answer.
• Know critical formulae
• Be aware that the correct answer is always there as it is one of the choices. If you aren’t arriving at the right answer, read the question again to understand it properly.
Here are GRE quantitative practice questions to illustrate MCQ style of questions across difficulty levels:

Difficulty level: Simple

If 8x+64 = 8-6x, what is the value of x?
1. -4
2. -56
3. 12
4. 7
5. 4

Solution

Equation given is 8x+64 = 8-6x.

Therefore the next step is 8x+6x = -64+8
Therefore the next step is 14x = -56
Hence x = -4
So the correct answer is a) -4

Difficulty level: Average

In the rectangle above, AB = x feet, BC = y feet, and AE = FC = 2 feet. What is the area of triangle DEF, in square feet?
1. xy − 2x − 2y + 4
2. xy − 2x − 2y − 4
3. xy/2− x − y + 2
4. xy/2−x−y-2
5. xy/2+2

Solution

Plug in values for x and y. If x = 4 and y = 5, then the sides of the triangle are 2 and 3.The area of a triangle = ½bh, so the triangle has an area of 3.
Plugging in the values in the choices presented, shows that only choice (c) evaluates to 3.

You could also do the same without plugging in values:
Area of the triangle = ½bh = ½(x-2)(y-2) = ½(xy-2x-2y+4) = ½xy-x-y+2.

Difficulty level: Challenging

There is a glass jar containing 60 jelly beans. Out of these 60 jelly beans, 22 are black, 18 are blue, 11 are orange, 5 are maroon and 4 are violet. Assume that a single jelly bean has to be chosen at random. Then what is the probability that the jelly bean will be neither maroon nor violet?
1. 0.09
2. 0.15
3. 0.54
4. 0.85
5. 0.91

Solution

As there are 4 violet jelly beans and 5 maroon jelly beans in a glass jar, there are 51 which were neither violet nor maroon. The probability of selecting one of these is 51 out of 60. 51/60 = 0.85. Therefore the correct answer is 0.85 which is option d.

## Multiple-choice Questions — Select One or More Answer Choices

This are MCQs where there could be one or more correct answer choices. Therefore, these questions present a different type of challenge.

Here are some handy tips to deal with MCQ – Select one or more answer choice

1. When tackling values which are within a range, try to figure out the minimum and maximum values. This will help you eliminate incorrect choices.
2. Be patient while working on these questions. Remember that there could be more than one correct answer for each question.

Here are the GRE quant practice questions to illustrate the type:

Difficulty level: Simple

Which two of the following numbers have a product that is between –1 and 0?
1. -20
2. -10
3. 2^-4
4. 3^-2

Solution

For this question, you must select a pair of answer choices. The product of the pair must be negative, so the possible products are (–20)(2–4), (–20)(3–2), (–10)(2–4), and (–10)(3–2). The product must also be greater than –1. The first product is The fraction with numerator negative 20 and denominator 2 to the power 4, equals the negative fraction with numerator 20 and denominator 16, which is less than negative 1., the second product is The fraction with numerator negative 20 and denominator 2 to the power 3, equals the negative fraction with numerator 20 and denominator 9, which is less than negative 1., and the third product is, The fraction with numerator negative 10 and denominator 2 to the power 4, equals the negative fraction with numerator 10 and denominator 16, which is greater than negative 1., so you can stop there. The correct answer consists of Choices B (–10) and C (2–4).

Difficulty level: Average

The average of 10 numbers is 7. Which of the following statements is true? Indicate all true statements.
1. The average increases by 1 if each number increases by 1
2. The average becomes 3 times, if each number becomes three times
3. If the sum of the numbers increases by 7, the average increases by 1
4. If seven numbers increase by 3 each and three numbers decrease by 7 each, the average remains the same
5. The sum of the numbers is 70

Solution

The challenge here is that you are not told how many of the statements are true. Therefore, you will have to examine each claim to figure out which ones are true and which are not.

Since the average of 10 numbers is 7, the sum of the numbers is 10*7 = 70.
1. If each number increases by 1, then the sum increases by 70+10=80
Average = 80/10=8
Average increases by 1
Option A is true.
2. If each number becomes three times, the sum also becomes three times.
Average = 3*70/10=3*7=21
Option B is true.
3. If the sum increases by 7, it becomes 70+7=77
Average = 77/10=7.7
Option C is false.
4. If 7 numbers increase by 3 and 3 decrease by 7, then sum = 70+7*3-3*7 = 70+21-21=70
Average = 70/10=7
Option D is true.
5. The sum of the numbers is 70
Average = 7 and number of observations = 10
Sum of observations = Average* number of observations = 7*10=70
Option E is also true.
Therefore, option A, B, D and E are true, and only one (C) is untrue.

Difficulty level: Challenging

Which of the following could be the unit’s digit of 57 to the power n where n is a positive integer?

Indicate all such digits:

0

1

2

3

4

5

6

7

8

9

Explanation

The unit’s digit of 57 to the power n is the same as the unit’s digit of 7 to the power n for all positive integers n. To see why this is true for n is equal to 2 compute 57 to the power 2 by hand and observe how its unit’s digit results from the unit’s digit of 7 to the power 2. Because this is true for every positive integer n, you need to consider only powers of 7. Beginning with n is equal to 1 and proceeding consecutively, the units digits of 7, 7 to the power 2 7 to the power 3 7 to the power 4 and 7 to the power 5 are 7, 9, 3, 1, and 7, respectively. In this sequence, the first digit, 7, appears again, and the pattern of four digits, 7, 9, 3, 1, repeats without end. Hence, these four digits are the only possible unit’s digits of 7 to the power and therefore of 57 to the power n. The correct answer consists of Choices B (1), D (3), H (7), and J (9).

## Numeric Entry Questions

The answer to these questions could either be an integer or decimal. It may even be a fraction. Integer and decimals can be entered in a single box and fractions in two separate boxes. You won’t have any choices to guide you.

Here are some handy tips to deal with Numeric Entry Questions

These types of questions require you to solve a word problem and enter your answer as an integer or a decimal in the answer box provided. A few questions may ask you to enter the answer as a fraction into two answer boxes presented instead. Here are some GRE quantitative practice test questions to illustrate the type:

• Be aware of the measurement units in use (km or miles).
• If you have to round an answer off then do so to its nearest degree. So 54.8 can be rounded off as 55 and 65.3 can be rounded off as 65.

Difficulty level: Simple

One pen costs \$0.25 and one marker costs \$0.35. At those prices, what is the total cost of 18 pens and 100 markers?

\$The answer space consists of a dollar sign, followed by a box for the answer.

Explanation

Multiplying \$0.25 by 18 yields \$4.50, which is the cost of the 18 pens; and multiplying \$0.35 by 100 yields \$35.00, which is the cost of the 100 markers. The total cost is therefore 4 dollars fifty cents, plus, thirty five dollars, plus, thirty nine dollars and fifty cents. Equivalent decimals, such as \$39.5 or \$39.500, are considered correct. Thus the correct answer is \$39.50 (or equivalent).

Difficulty level: Average

Rectangle R has length 30 and width 10, and square S has length 5. The perimeter of S is what fraction of the perimeter of R ?

The answer space consists of a fraction bar, and two boxes, one above and one below the fraction bar.

Explanation

The perimeter of R is Thirty, plus ten, plus, thirty, plus ten, equals eighty. and the perimeter of S is 4 times 5 = 20 Therefore, the perimeter of S is 20 over 80 of the perimeter of R. To enter the answer 20 over 80 you should enter the numerator 20 in the top box and the denominator 80 in the bottom box. Because the fraction does not need to be reduced to lowest terms, any fraction that is equivalent to 20 over 80 is also considered correct, as long as it fits in the boxes. For example, both of the fractions 2 eighths and 1 fourth are considered correct. Thus the correct answer is 20 over 80 (or any equivalent fraction).

Difficulty level: Challenging

Working alone at its constant rate, machine A produces k liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces k liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k liters of the chemical?

The answer space consists of a fraction bar, and two boxes, one above and one below the fraction bar.

Solution:

• Machine A produces (k/ 10) liters per minute.
• Machine B produces (k /15) liters per minute.
• When working simultaneously, the rate at which the chemical is produced is the sum of these two rates, which is (k/10) +(k /15)= k(1/10 + 1/15) =k(25/150) = (k/6 ).
• To compute the time required to produce k liters at this rate, divide the amount k by the rate (k/6) = k / (k/6) = 6
• Therefore, the correct answer is 6 minutes (or equivalent).

This was just a glimpse into the different types of questions you will face in the GRE math section. Each of the sections would have three data interpretation sets, and the rest of the questions would be independent.

If you get an answer wrong during your GRE Quant practice, figure out where you went wrong. Your proficiency in each section would be different, and accordingly you may want to allocate different study times for each type of question.

We recommend that you start with GRE quantitative practice tests before you move on to GRE practice tests as a whole. This will allow you to refine your time management techniques for each section. Follow the LPF method for GRE Quant preparation for the best results:

• LEARN: Get a holistic understanding by breaking down the GRE Quant syllabus into simple, easily understandable concepts like Permutations & Combinations or Geometry. Learn the specific techniques to tackle questions from the topic you have selected.
• PRACTICE: Take a GRE quantitative practice test as soon as you are done learning a particular concept. With GRE-style questions for specific concepts, you would know how deep your understanding of the topic is.
• FEEDBACK: Get immediate feedback after every practice test that you take.

• Practice GRE Quant questions in a serene environment.
• Remember to use your calculator to save time rather than manually solving operations.
• Memorise important formulae, squares upto 30 and cubes upto 10.
• Challenge yourself when it comes to the time limit. For example, if each section of the real GRE Quant Test is for 35 minutes, try to solve as many possible within 33 minutes.
• The only way to get better at GRE Quant is to keep practising regularly.
• Check out the explanation and answers only after solving the entire test paper.

Question 1: What is GRE Quant?

Answer 1: The Quantitative section of the GRE comprises fifty percent of the exam and is designed to gauge your grasp over basic mathematical concepts and formulae, as well as your ability to reason analytically using quantitative tools. The good news is that, most of the concepts you need to conquer the Quants section were taught to you in school, which generally means that students from STEM backgrounds find it easier to sail through the Quants syllabus.

Question 2: How is 170 Quant scored in GRE?

Answer 2: These are some of the steps:

1. Understand the Syllabus & Exam Pattern.
4. Focus on giving topic-wise tests.
5. Start working on advance level questions.
6. Give full length mocks and evaluate them at every step.
7. Every 170 scorer ensures that they are giving enough time to analyze their mocks and work on their shortcomings.

Question 3: Can we use a calculator in the GRE?

Answer 3: ETS provides an on screen calculator during your GRE Quant.

Question 4: How do I study for GRE quantitative?

Answer 4: These are some of the steps:

1. Understand the Syllabus & Exam Pattern.
4. Focus on giving topic-wise tests.
5. Start working on advance level questions.
6. Give full length mocks and evaluate them at every step.

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