GRE Quantitative Reasoning
Master Quantitative Comparison, Problem Solving, and Data Sufficiency with comprehensive topic coverage and 12 practice questions with step-by-step solutions.
4 Question Types
Quantitative Comparison
Compare Column A with Column B. Answer: A > B, B > A, equal, or cannot determine
Strategy:
Never plug in numbers—use algebra. Eliminate answer choices. If both columns can be positive and negative, answer is usually "cannot determine"
Example: Column A: 3x + 5 | Column B: 2x + 8 where 0 < x < 5. Answer: Cannot determine (depends on value of x)
Multiple Choice (Select One)
Choose the single best answer from 5 options
Strategy:
Plug in answer choices starting with (C). Use estimation and pattern recognition to eliminate obviously wrong answers.
Example: What is 20% of 150? A) 25 B) 30 C) 40 D) 75 E) 120. Answer: B (0.20 × 150 = 30)
Multiple Choice (Select One or More)
Select ALL answer choices that fit the criteria
Strategy:
Test each option systematically. Don't assume there's only one right answer. Some have 2-3 correct choices.
Example: Which of the following are prime numbers? A) 2 B) 13 C) 21 D) 29 E) 35. Answer: A, B, D
Numeric Entry
Type in your answer (integer, decimal, or fraction)
Strategy:
Be precise. If asking for probability, remember answer is between 0 and 1. Round only if instructed.
Example: If 5x = 20, what is x? Answer: 4
Topics Covered
Arithmetic
- ✓Integers, fractions, decimals, percentages
- ✓Ratio and proportion
- ✓Exponents and roots
- ✓Order of operations
Algebra
- ✓Linear equations and inequalities
- ✓Systems of equations
- ✓Quadratic equations
- ✓Functions and coordinate geometry
Geometry
- ✓Lines, angles, and triangles
- ✓Quadrilaterals and circles
- ✓3D figures (volume, surface area)
- ✓Coordinate geometry
Data Analysis
- ✓Mean, median, mode, range
- ✓Standard deviation and normal distribution
- ✓Probability
- ✓Data interpretation from tables/graphs
12 Practice Questions
Question 1
If 40% of a number is 16, what is the number?
Question 2
Column A: The average of 5, 10, and 15 | Column B: The median of 5, 10, 15, 20, and 25
Question 3
If x² - 7x + 12 = 0, what are the possible values of x?
Question 4
A triangle has sides of length 5, 12, and 13. Is it a right triangle?
Question 5
If the probability of event A is 0.3 and probability of event B is 0.5, and they are independent, what is the probability of both A and B occurring?
Question 6
If a circle has diameter 10, what is its area?
Question 7
x is a positive integer. Column A: x² | Column B: 2x
Question 8
The ratio of boys to girls in a class is 3:2. If there are 15 boys, how many girls are there?
Question 9
What is the standard deviation of the dataset: 2, 4, 6, 8, 10?
Question 10
If 3x + 2 = 14, what is x?
Question 11
A store sells shirts for $20 each. If there's a 25% discount, what is the sale price?
Question 12
Column A: √16 | Column B: ³√27
Quantitative Comparison Strategies
1Never plug in numbers. Use algebra to determine the relationship.
2If you can find even one case where A > B and one case where B > A, answer is "Cannot determine".
3Extreme cases often help. Try 0, negative numbers, fractions, and large numbers.
4"Cannot determine" is a valid answer—roughly 1/3 of QC questions have this answer.
5Read carefully. "x > 0" changes the problem significantly.