Ch3. GRE Quantitative — Comparison Strategy & Data Interpretation

GRE Quantitative Overview

27 questions, 47 minutes, on-screen calculator available.

Question types:

Quantitative Comparison (QC): Compare two quantities
Problem Solving: 5-choice or numeric entry
Data Interpretation: Graph and table analysis sets

Quantitative Comparison Strategy

QC is unique to the GRE. Your task: determine which of two quantities (A or B) is larger — or whether they’re equal or indeterminate.

The 4 fixed answer choices:

(A) Quantity A is greater
(B) Quantity B is greater
(C) The two quantities are equal
(D) The relationship cannot be determined from the information given

QC Golden Rules

Simplify both columns algebraically before comparing
Test special values: 0, 1, −1, fractions, large numbers, and negatives
Add or subtract the same amount from both sides — relationship unchanged
Multiply by a positive — relationship unchanged. Multiply by a negative — FLIP the inequality

Core Math Concepts

Number Theory

Primes: 2, 3, 5, 7, 11… (2 is the only even prime)
Absolute value: |x| ≥ 0
Exponents: aᵐ × aⁿ = aᵐ⁺ⁿ; (aᵐ)ⁿ = aᵐⁿ

Algebra

Sum of roots of quadratic ax² + bx + c = 0: −b/a
Product of roots: c/a

Geometry

Pythagorean theorem: a² + b² = c²
Circle: area = πr², circumference = 2πr
Triangle area = ½ × base × height

Statistics

Mean = sum / count
Range = max − min

Probability

P(A or B) = P(A) + P(B) − P(A∩B)
Independent events: P(A and B) = P(A) × P(B)

Data Interpretation Strategy

Graph and table sets appear in groups of 2–4 questions.

Essential skills:

Ratio/proportion: Denominator always matters
Percent change: (New − Old) / Old × 100
Estimation: “Approximately” means you don’t need to be exact

Common traps:

Y-axis units (thousands, millions, percentages)
Connecting data across multiple graphs
Year-over-year vs. total comparisons

Practice Questions

Q1 (QC). x > 0
Column A: x + 1/x
Column B: 2

Analyze: By AM-GM inequality, x + 1/x ≥ 2 (equality when x = 1).
If x = 1: A = 2 = B. If x = 2: A = 2.5 > B.
Answer: A (since x > 0 and x ≠ 0 must hold, but x = 1 gives equality → actually not A always greater… Answer: A, because AM-GM says minimum is 2 achieved at x=1, so A ≥ 2 always, meaning A ≥ B with equality possible → D when considering equality)

Q2. 6 people sit in a circular arrangement. How many distinct arrangements?

Answer: (6−1)! = 5! = 120

Chapter 4 Preview

Next: GRE Analytical Writing — Issue Essay and Argument Essay structure, scoring rubrics, and templates for a 4.5+ score.