GRE Quantitative (Math) Reasoning: Definition, Question Types, Problems, and Practice Questions
The Quantitative Reasoning section of the GRE assesses a test taker’s basic mathematical skills, understanding of elementary mathematical concepts, and the ability to reason quantitatively and to model and solve problems with quantitative methods.
What are the 4 content areas of the GRE Quantitative Reasoning Section?
The 4 content areas of the GRE Quantitative Reasoning section and the skills, concepts, and abilities it assess are listed below:
1. Arithmetic
- Properties and types of integers, such as divisibility, factorization, prime numbers, remainders and odd and even integers
- Arithmetic operations, exponents and roots
- Concepts such as estimation, percent, ratio, rate, absolute value, the number line, decimal representation and sequences of numbers
2. Algebra
- Operations with exponents
- Factoring and simplifying algebraic expressions
- Relations, functions, equations and inequalities
- Solving linear and quadratic equations and inequalities
- Solving simultaneous equations and inequalities
- Setting up equations to solve word problems
- Coordinate geometry, including graphs of functions, equations and inequalities
- Intercepts and slopes of lines
3. Geometry
- Parallel and perpendicular lines
- Circles
- Triangles — including isosceles, equilateral and 30°-60°-90° triangles
- Quadrilaterals
- Other polygons
- Congruent and similar figures
- Three-dimensional figures
- Area
- Perimeter
- Volume
- The Pythagorean theorem and angle measurement in degrees
4. Data analysis
- Basic descriptive statistics, such as mean, median, mode, range, standard deviation, interquartile range, quartiles and percentiles
- Interpretation of data in tables and graphs, such as line graphs
- Bar graphs, circle graphs, box plots, scatter plots and frequency distributions
- Elementary probability, such as probabilities of compound events and independent events
- Conditional probability
- Random variables and probability distributions, including normal distribution
- Counting methods, such as combinations, permutations and Venn diagrams
The lists above are the content areas of the GRE Quantitative Reasoning section. This covers the skills, concepts, and abilities it assesses. Putting emphasis on these particular topics during the preparation process will help examinees obtain high scores in this section.
What are the GRE Quantitative Reasoning Question Types?
Quantitative Comparison, Multiple Choice – Select One Answer Choice, Multiple Choice – Select One or More Answer Choice, and Numeric Entry are the GRE Quantitative Reasoning question types.
1. Quantitative Comparison Question Type
The Quantitative Comparison type of question asks a test taker to compare two quantities and determine which of the statements below describes the comparison.
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Quantitative Comparison Question Type Sample Questions with Answers
Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question.
Sample Question 1:
Quantity A |
Quantity B |
---|---|
The least prime number greater than 24 |
The greatest prime number less than 28 |
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Correct Answer: The correct answer is Choice A, Quantity A is greater.
Explanation: For the integers greater than 24, note that 25, 26, 27, and 28 are not prime numbers, but 29 is a prime number, as are 31 and many other greater integers. Thus, 29 is the least prime number greater than 24, and Quantity A is 29. For the integers less than 28, note that 27, 26, 25, and 24 are not prime numbers, but 23 is a prime number, as are 19 and several other lesser integers. Thus, 23 is the greatest prime number less than 28, and Quantity B is 23.
Sample Question 2:
Lionel is younger than Maria. | |
---|---|
Quantity A |
Quantity B |
Twice Lionel’s age |
Maria’s age |
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Correct Answer: The correct answer is Choice D, the relationship cannot be determined from the information given.
Explanation: If Lionel’s age is 6 years and Maria’s age is 10 years, then Quantity A is greater, but if Lionel’s age is 4 years and Maria’s age is 10 years, then Quantity B is greater. Thus, the relationship cannot be determined.
Sample Question 3:
Quantity A |
Quantity B |
---|---|
54% of 360 |
150 |
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Correct Answer: The correct answer is Choice A, Quantity A is greater.
Explanation: Without doing the exact computation, you can see that 54 percent of 360 is greater than of 360, which is 180, and 180 is greater than Quantity B, 150.
2. Multiple Choice – Select One Answer Question Type
The Multiple Choice – Select One Answer type of question is similar to the traditional multiple choice of selecting one answer from a list of five choices.
Multiple Choice – Select One Answer Question Type Sample Questions with Answers
Directions: Select a single answer choice.
Sample Question 1: If 5x + 32 = 4 – 2x, what is the value of x ?
- -4
- -3
- 4
- 7
- 12
Correct Answer: The correct answer is Choice A, Negative 4.
Explanation: Solving the equation for x, you get 7x = -28, and so x = -4.
Sample Question 2: A certain jar contains 60 jelly beans — 22 white, 18 green, 11 yellow, 5 red, and 4 purple. If a jelly bean is to be chosen at random, what is the probability that the jelly bean will be neither red nor purple?
- 0.09
- 0.15
- 0.54
- 0.85
- 0.91
Correct Answer: The correct answer is Choice D, 0.85.
Explanation: Since there are 5 red and 4 purple jelly beans in the jar, there are 51 that are neither red nor purple and the probability of selecting one of these is . Since all of the answer choices are decimals, you must convert the fraction to its decimal equivalent, 0.85.
Sample Question 3: A car got 33 miles per gallon using gasoline that cost $2.95 per gallon. Approximately what was the cost, in dollars, of the gasoline used in driving the car 350 miles?
- $10
- $20
- $30
- $40
- $50
Correct Answer: The correct answer is Choice C, $30.
Explanation: The car used gallons of gasoline, so the cost was dollars. You can estimate the product by estimating a little low, 10, and estimating 2.95 a little high, 3, to get approximately (10)(3) = 30 dollars. You can also use the calculator to compute a more exact answer and then round the answer to the nearest 10 dollars, as suggested by the answer choices. The calculator yields the decimal 31.287… which rounds to 30 dollars.
3. Multiple Choice – Select One or More Answer Question Type
The Multiple Choice – Select One or More Answer type of question asks a test taker to select one or more from a list of choices. Also, some questions do not indicate how many choices to select.
Multiple Choice – Select One or More Answer Question Type Sample Questions with Answers
Directions: Select one or more answer choices according to the specific question directions. If the question does not specify how many answer choices to select, select all that apply.
- The correct answer may be just one of the choices or as many as all of the choices, depending on the question.
- No credit is given unless you select all of the correct choices and no others.
If the question specifies how many answer choices to select, select exactly that number of choices.
Sample Question 1: Which of the following integers are multiples of both 2 and 3?
Indicate all such integers.
- 8
- 9
- 12
- 18
- 21
- 36
Correct Answers: Choices C (12), D (18), and F (36).
Explanation: You can first identify the multiples of 2, which are 8, 12, 18, and 36, and then among the multiples of 2 identify the multiples of 3, which are 12, 18, and 36. Alternatively, if you realize that every number that is a multiple of 2 and 3 is also a multiple of 6, you can identify the choices that are multiples of 6.
Sample Question 2: Which of the following could be the unit 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
Correct Answers: The correct answer consists of Choices B (1), D (3), H (7), and J (9).
Explanation: The units digit of 57n is the same as the units digit of 7n for all positive integers n. To see why this is true for n=2, compute 572 by hand and observe how its unit digit results from the unit digit of 72. Because this is true for every positive integer n, you need to consider only powers of 7. Beginning with n=1 and proceeding consecutively, the units digits of 7, 72, 73, 74 and 75 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 units digits of 7n and therefore of 57n.
Sample Question 3: Which two of the following numbers have a product that is between –1 and 0? Indicate both of the numbers.
- –20
- –10
- 2 –4
- 3 –2
Correct Answer: The correct answer consists of Choices B (–10) and C (2–4).
Explanation: 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 second product is , so you can stop there.
4. Numeric Entry Question Type
The Numeric Entry type of questions ask examinees to either input their answer as an integer or a decimal in a single answer box, or to enter it as a fraction in two separate boxes, one each for the numerator and denominator. It is used in the computer-adaptive version of the test where test takers use a mouse and keyboard to enter their answer.
Numeric Entry Question Type Sample Questions with Answers
Directions: Enter your answer as an integer or a decimal if there is a single answer box OR as a fraction if there are two separate answer boxes — one for the numerator and one for the denominator.
To enter an integer or a decimal, either type the number in the answer box using the keyboard or use the Transfer Display button on the calculator.
- First, select the answer box — a cursor will appear in the box — and then type the number.
- For a negative sign, type a hyphen. For a decimal point, type a period.
- The Transfer Display button on the calculator will transfer the calculator display to the answer box.
- Equivalent forms of the correct answer, such as 2.5 and 2.50, are all correct.
- Enter the exact answer unless the question asks you to round your answer.
To enter a fraction, type the numerator and the denominator in their respective answer boxes using the keyboard.
- Select each answer box — a cursor will appear in the box — then type an integer. A decimal point cannot be used in either box.
- For a negative sign, type a hyphen; in either box.
- The Transfer Display button on the calculator cannot be used for a fraction.
- Fractions do not need to be reduced to lowest terms, though you may need to reduce your fraction to fit in the boxes.
Sample Question 1: 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?
$
Correct Answer: The correct answer is $39.50 (or equivalent).
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 $4.50 + $35.00 = $39.50. Equivalent decimals, such as $39.5 or $39.500, are considered correct.
Note that the dollar symbol is in front of the answer box, so the symbol $ does not need to be entered in the box. In fact, only numbers, a decimal point and a negative sign can be entered in the answer box.
Sample Question 2: 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 ?
Correct Answer: Thus the correct answer is (or any equivalent fraction).
Explanation: The perimeter of R is 30 + 10 + 30 +10 = 80, and the perimeter of S is (4)(5) = 20. Therefore, the perimeter of S is of the perimeter of R. To enter the answer 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 is also considered correct, as long as it fits in the boxes. For example, both of the fractions and are considered correct.
Sample Question 3: A merchant made a profit of $5 on the sale of a sweater that cost the merchant $15. What is the profit expressed as a percent of the merchant’s cost? Give your answer to the nearest whole percent.
%
Correct Answer: The correct answer is 33% (or equivalent).
Explanation: The percent profit is percent, which is 33%, to the nearest whole percent.
If you use the calculator and the Transfer Display button, the number that will be transferred to the answer box is 33.333333, which is incorrect since it is not given to the nearest whole percent. You will need to adjust the number in the answer box by deleting all of the digits to the right of the decimal point.
Also, since you are asked to give the answer as a percent, the decimal equivalent of 33 percent, which is 0.33, is incorrect. The percent symbol next to the answer box indicates that the form of the answer must be a percent. Entering 0.33 in the box would give the erroneous answer 0.33%.
What is the Data Interpretation Set?
The Data Interpretation questions ask a test taker to interpret or analyze data grouped together, in a table, graph or other data presentation. These questions may be Multiple Choice or Numeric Entry.
Data Interpretation Set Sample Questions with Answers
Directions: Questions 1 to 3 are based on the following data.
Annual Percent Change in Dollar Amount of Sales at Five Retail Stores from 2006 to 2008 | ||
---|---|---|
Store |
Percent Change from 2006 to 2007 |
Percent Change from 2007 to 2008 |
P |
10 |
-10 |
Q |
-20 |
9 |
R |
5 |
12 |
S |
-7 |
-15 |
T |
17 |
-8 |
Sample Question 1: If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- $727,200
- $792,000
- $800,000
- $880,000
- $968,000
Correct Answer: The correct answer is Choice B, $792,000.
Explanation: According to the table above, if the dollar amount of sales at Store P was $800,000 for 2006, then it was 10 percent greater for 2007, which is 110 percent of that amount, or $880,000. For 2008 the amount was 90 percent of $880,000, which is $792,000. Note that an increase of 10 percent for one year and a decrease of 10 percent for the following year does not result in the same dollar amount as the original dollar amount because the base that is used in computing the percentage is $800,000 for the first change but $880,000 for the second change.
Sample Question 2: At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1 percent.
%
Correct Answer: The correct answer is 108.7% (or equivalent).
Explanation: If A is the dollar amount of sales at Store T for 2007, then 8 percent of A, or 0.08A, is the amount of decrease from 2007 to 2008. Thus A-0.08A =0.92A is the dollar amount for 2008. Therefore, the desired percent can be obtained by dividing A by 0.92A, which equals Expressed as a percent and rounded to the nearest 0.1 percent, this number is 108.7%.
Sample Question 3: Based on the information given, which of the following statements must be true? Indicate all such statements.
- For 2008 the dollar amount of sales at Store R was greater than that at each of the other four stores.
- The dollar amount of sales at Store S for 2008 was 22 percent less than that for 2006.
- The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006.
Correct Answer: The correct answer consists of only Choice C – The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006.
Explanation: For Choice A, since the only data given in the table are percent changes from year to year, there is no way to compare the actual dollar amount of sales at the stores for 2008 or for any other year. Even though Store R had the greatest percent increase from 2006 to 2008, its actual dollar amount of sales for 2008 may have been much smaller than that for any of the other four stores, and therefore Choice A is not necessarily true.
For Choice B, even though the sum of the two percent decreases would suggest a 22 percent decrease, the bases of the percentages are different. If B is the dollar amount of sales at Store S for 2006, then the dollar amount for 2007 is 93 percent of B, or 0.93B, and the dollar amount for 2008 is given by (0.85)(0.93)B, which is 0.7905B. Note that this represents a percent decrease of 100-79.05=20.95 percent, which is not equal to 22 percent, and so Choice B is not true.
For Choice C, if C is the dollar amount of sales at Store R for 2006, then the dollar amount for 2007 is given by 1.05C and the dollar amount for 2008 is given by (1.12)(1.05)C which is 1.176C. Note that this represents a 17.6 percent increase, which is greater than 17 percent, so Choice C must be true.
What is on the GRE Quantitative Reasoning and how long does it take?
The GRE Quantitative Reasoning has two sections with 20 questions each. Each section may be taken for 35 minutes.
How is the GRE Quantitative Reasoning Measure scored?
The Quantitative Reasoning Score is based on the test taker’s number of correct responses to the questions. It will also reflect the difficulty of each level section. The score may range from 130 being the lowest to 170 as the highest in 1-point increments. Based on recorded data, the average GRE Quantitative Score is 152.57.
What is a good GRE Quantitative Reasoning score?
A score of 160 in the GRE Quantitative Reasoning section is a good score. A test taker who obtained this score falls in the 75th percentile which means he scored above 75% of the total test takers. On the other hand, a score of 166 is an excellent one. This puts an examiner on the 90th percentile which will help to be a strong candidate for most programs.
What is a low or bad GRE Quantitative Reasoning score?
A score of below 154 in the GRE Quantitative Reasoning section is a bad score. A test taker who obtained this score falls in the 50th percentile which means he scored below 50% of the total test takers. On the other hand, a score of 147 is worse. This puts an examiner on the 25th percentile which will help reflect badly on the overall GRE score.
Do GRE prep courses help with Quantitative Reasoning?
Yes, GRE preparation courses are specifically designed to enhance a student’s proficiency in various sections of the exam, including Quantitative Reasoning. These courses provide structured content, practice problems, and test-taking strategies tailored to the Quant section. By participating, students often gain a deeper understanding of mathematical concepts, improve problem-solving speed, and build confidence. Regular practice and expert guidance from these courses can significantly boost one’s performance in Quantitative Reasoning.
References:
- https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/comparison/sample_questions
- https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/multiple_choice_one/sample_questions
- https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/multiple_choice_more/sample_questions
- https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/numeric_entry/sample_questions
- https://www.ets.org/gre/revised_general/prepare/quantitative_reasoning/data_interpretation/sample_questions