Arithmetic Summary

GRE Quantitative · Axiom Academy

Tying together number properties, fractions/decimals/percents, ratios, exponents & roots, the number line, and estimation into one GRE-ready toolkit. Number properties are the GRE's favorite disguise. Even/odd, prime, divisibility, and remainder questions rarely look like number-theory questions — they hide inside word problems and quantitative comparisons. Fractions, decimals, and percents are one idea in three costumes. Fluently converting between them — and multiplying successive percent changes instead of adding them — is worth more than any single formula. Ratios and proportions are about relationships, not raw values — set up matching units, cross-multiply, and scale. Exponent and root rules only combine when the base matches — convert to a common base first, and remember that a fractional exponent is a root. The number line orders everything — including negatives and fractions — and absolute value equations almost always split into two cases. Estimate on purpose, not by accident: it's a fast way to eliminate answers when choices are spread out, and a trap when they're close together. Core Concept Number Properties & Divisibility Even/odd rules, prime numbers, divisibility, and remainders form the backbone of GRE "number properties" questions. The highest-leverage trick: remainders of a power expression cycle, so you never need to compute the full power — just find the cycle and locate your exponent's position in it.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.