M01 | Lesson 1: Integers, Odd/Even, Absolute Value & PEMDAS

The Core Idea

An integer is any whole number — positive, negative, or zero. The set goes: ..., −3, −2, −1, 0, 1, 2, 3, ... No fractions. No decimals. The GRE builds a substantial portion of its Quant sections on how these numbers add, multiply, behave under exponents, and interact with absolute value. This is the foundation everything else sits on. Get it shaky here, and every downstream topic pays for it.

How It Shows Up

Parity and sign reasoning are constant in Quantitative Comparison questions — the ones where you're comparing two expressions without knowing the exact values of the variables. A question will tell you x < 0 and y > 0 and ask you to compare x²y with xy². You need to determine the sign of each expression without picking numbers, and you need to do it fast. Absolute value appears in both QC and Problem Solving, usually designed to obscure whether the original value was positive or negative. PEMDAS errors show up at every difficulty level — a wrong order of operations is a clean miss on a question you otherwise understood. Number properties account for roughly 4 questions per Quant section, meaning 8 across your full test.

The Rule

Integers: {..., −3, −2, −1, 0, 1, 2, 3, ...} — no fractions, no decimals.

Zero: even; neither positive nor negative; anything × 0 = 0; 0 ÷ (any nonzero number) = 0; division by zero is undefined.

One: neither prime