Estimation and Approximation Techniques

GRE Quantitative · Axiom Academy

LESSON Estimation and Approximation The GRE rarely needs an exact answer — round to friendly numbers and the right choice usually jumps right out. The core move is simple: replace an ugly number with a nearby one you can compute in your head. 37% becomes a third . 198 becomes 200 . Watch the messy expression get rounded piece by piece into something you can solve without a calculator. The exact calculation — slow, and unnecessary here The rounded estimate — fast, and close enough 2. The Estimate Finds the Right Choice Here's why this matters on a real question. If x = 1.98 and y = 3.1 , approximately what is 2xy ? Round x down to 2 and y down to 3 — then 2xy ≈ 2 × 2 × 3 = 12 . Watch the estimate travel onto the number line: it doesn't need to be exact, it just needs to land closer to one choice than to any other. x ≈ 2, y ≈ 3 — round each factor first 3. When the Choices Are Close, Estimate Carefully Estimation wins when the answer choices are spread out — it can fail when they're packed close together . Take "which is closest to 31% of 313?" with choices 95, 97, 99, 101. Round crudely to 30% of 300 = 90, and the estimate actually lands nearest the wrong choice. The gap between neighboring choices is smaller than the rounding error itself. What went wrong: 31% of 313 is exactly 97.03, so (B) 97 is correct. But rounding both numbers down (31%→30%, 313→300) throws away just enough to land at 90 — closer to (A) 95 than to the true answer (B) 97.

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