Quantitative Ability
Arithmetic and percent
Percent problems fail on wording, not computation. Distinguish "20% of X" from "X is 20% more than Y," and remember that successive percent changes multiply: a 20% rise followed by a 20% fall gives 1.2 × 0.8 = 0.96, a net 4% decrease, not zero.
Rate, work, and mixtures
For work problems, add rates - 1/6 + 1/12 = 1/4, so together the job takes 4 hours - never add times. For distance problems, convert units before substituting. For mixtures, track the amount of the pure substance, not just total volume.
Algebra and number properties
Factor before expanding. Know divisibility tests: 3 and 9 by digit sum, 4 by the last two digits, 11 by the alternating digit sum. For LCM and GCD, prime-factorize first.
Geometry
Memorize area and volume formulas plus the common Pythagorean triples (3-4-5, 5-12-13, 8-15-17). Triangle angles sum to 180°, and an exterior angle equals the sum of the two remote interior angles.
Data interpretation
Read axis labels and units before calculating. Percentages taken of different bases are not comparable.
Rule of thumb
Estimate the answer before computing. If your exact result is far from the estimate, the setup is wrong - not the arithmetic.