GRE Quantitative Reasoning Practice Questions Practice Questions with Answers

Concept Explanation

GRE Quantitative Reasoning practice questions evaluate your ability to solve problems using mathematical models and quantitative methods across arithmetic, algebra, geometry, and data analysis. These questions are not merely about memorizing formulas; they test your logical reasoning and your capacity to apply mathematical concepts in various contexts. The exam features four main question types: Quantitative Comparison, Multiple-choice (Select One), Multiple-choice (Select One or More), and Numeric Entry. Understanding the underlying structures of these problems is essential for achieving a competitive score on the GRE Prep journey.

Success in this section requires a solid grasp of high school-level mathematics, typically covering topics found in standard mathematics curricula. While the calculator provided on-screen can assist with complex arithmetic, the most efficient test-takers often use mental math and estimation to save time. Key areas of focus include number properties, linear and quadratic equations, coordinate geometry, and statistical measures like mean, median, and standard deviation.

Solved Examples

Reviewing worked examples helps clarify how to approach different question formats and identify common traps set by test-makers.

1. Quantitative Comparison Example:
   Quantity A: $2x + 5$
   Quantity B: $3x - 2$
   Condition: $x > 7$
   Solution:
   1. Subtract $2x$ from both quantities. Quantity A becomes 5; Quantity B becomes $x - 2$.
   2. Add 2 to both quantities. Quantity A becomes 7; Quantity B becomes $x$.
   3. Since the condition states $x > 7$, Quantity B is always greater than Quantity A.
   4. Answer: Quantity B is greater.
2. Algebraic Word Problem:
   A car travels at an average speed of 60 miles per hour for 3 hours and then at 45 miles per hour for 2 hours. What is the average speed for the entire 5-hour trip?
   Solution:
   1. Calculate total distance: $(60 \times 3) + (45 \times 2) = 180 + 90 = 270$ miles.
   2. Calculate total time: $3 + 2 = 5$ hours.
   3. Apply the average speed formula: $\text{Average Speed} = \frac{ \text{Total Distance}}{ \text{Total Time}}$.
   4. $\frac{270}{5} = 54$ miles per hour.
   5. Answer: 54 mph.
3. Geometry Example:
   The area of a circle is $16\pi$. What is the circumference of the circle?
   Solution:
   1. Use the area formula $A = \pi r^2$ to find the radius: $16\pi = \pi r^2$.
   2. Divide by $\pi$ and take the square root: $r^2 = 16$, so $r = 4$.
   3. Use the circumference formula $C = 2\pi r$.
   4. $C = 2\pi(4) = 8\pi$.
   5. Answer: $8\pi$.

Practice Questions

1. If $3x - 7 = 14$, what is the value of $x + 5$?
2. A bag contains 4 red marbles, 6 blue marbles, and 10 green marbles. If one marble is picked at random, what is the probability that it is NOT blue?
3. Quantity A: The remainder when 51 is divided by 7.
   Quantity B: The remainder when 65 is divided by 8.

4. A rectangular garden has a length that is 3 feet longer than its width. If the perimeter is 46 feet, what is the area of the garden in square feet?
5. If $a < b < 0$, which of the following must be true? (Select all that apply)
   A) $ab > 0$
   B) $a + b > 0$
   C) $a^2 > b^2$
6. The average (arithmetic mean) of five numbers is 20. If a sixth number, 32, is added to the set, what is the new average?
7. Quantity A: $(2^3)^2$
   Quantity B: $2^3 \times 2^2$
8. A laptop originally priced at $800 is on sale for 15% off. If an additional 10% discount is applied to the sale price, what is the final price?
9. In a group of 100 students, 60 study French, 40 study Spanish, and 20 study both. How many students study neither language?
10. If the side of a square is increased by 20%, by what percentage does the area increase?

Answers & Explanations

1. Answer: 12. Solve for $x$: $3x = 21$, so $x = 7$. Then, $x + 5 = 7 + 5 = 12$.
2. Answer: 0.7 (or 7/10). Total marbles = $4 + 6 + 10 = 20$. Marbles that are NOT blue = $4 + 10 = 14$. Probability = $\frac{14}{20} = 0.7$.
3. Answer: Quantity A is greater. For Quantity A: $51 = (7 \times 7) + 2$, so remainder is 2. For Quantity B: $65 = (8 \times 8) + 1$, so remainder is 1. Since $2 > 1$, A is greater.
4. Answer: 130. Let width be $w$ and length be $w+3$. Perimeter $P = 2(w + w + 3) = 46$. $4w + 6 = 46 \rightarrow 4w = 40 \rightarrow w = 10$. Length = 13. Area = $10 \times 13 = 130$.
5. Answer: A and C. A is true because the product of two negative numbers is positive. B is false because the sum of two negatives is negative. C is true because a smaller negative number (like -5) has a larger square (25) than a larger negative number (like -2 squared is 4).
6. Answer: 22. Sum of first five = $20 \times 5 = 100$. New sum = $100 + 32 = 132$. New average = $\frac{132}{6} = 22$.
7. Answer: Quantity A is greater. Quantity A = $2^6 = 64$. Quantity B = $2^5 = 32$.
8. Answer: $612. First discount: $800 \times 0.85 = 680$. Second discount: $680 \times 0.90 = 612$.
9. Answer: 20. Using the formula $|A \cup B| = |A| + |B| - |A \cap B|$: Students studying at least one = $60 + 40 - 20 = 80$. Neither = $100 - 80 = 20$.
10. Answer: 44%. Let original side be $s$. New side is $1.2s$. New area = $(1.2s)^2 = 1.44s^2$. This represents a 44% increase over the original area $s^2$.

1. If the ratio of boys to girls in a class is 3:5 and there are 40 students total, how many girls are in the class?

• A15
• B24
• C25
• D30

Frequently Asked Questions

What topics are covered in the GRE Quantitative Reasoning section?

The section covers arithmetic, algebra, geometry, and data analysis based on mathematical concepts typically taught in high school. It does not include advanced topics like trigonometry or calculus.

Can I use a calculator on the GRE Quant section?

Yes, an on-screen calculator is provided during the computer-delivered test for basic arithmetic operations. However, it is often faster to use mental math for simple calculations or to use the AI Flashcard Generator to memorize common squares and square roots.

What is a good score for GRE Quantitative Reasoning?

Scores range from 130 to 170 in one-point increments. A "good" score depends on your target graduate program, but highly competitive STEM programs often look for scores above 165.

How is the GRE Quant section structured?

The section is section-level adaptive, meaning your performance on the first math section determines the difficulty of the second. Each section contains roughly 20 questions to be completed in 35 minutes.

How can I improve my speed on GRE math questions?

Improving speed requires consistent practice with timed sets and learning to recognize patterns in questions. Utilizing tools like the AI Question Generator can provide unlimited practice to build the necessary familiarity with problem types.