Quantitative Reasoning
Quantitative Reasoning tests numerical fluency under time pressure: arithmetic, percentages, ratios, averages, number series, and short data sets. Most questions reward setting up the calculation cleanly rather than doing lengthy arithmetic. Watch the units and the base of every percentage.
Number series
Check first differences, then ratios, then second differences. Also test alternating rules (two interleaved sequences), squares and cubes, and primes. Do not settle for a pattern that fits only the last two terms; verify it against the whole series.
Percentages and ratios
A 25% fall followed by a 10% fall is not a 35% fall, because the second percentage applies to the reduced price. Percentage points measure the arithmetic difference between two percentages; percent measures relative change. In ratios, convert to the same unit and identify whether the question asks for a part or the whole.
Averages
Total = mean × number of items. For a weighted average, multiply each group mean by its size, add, and divide by the total size; a simple average of the two means is wrong unless the groups are equal.
Worked example: A jacket costs $80. It is reduced by 25%, then the sale price is reduced by a further 10%. Final price? 80 × 0.75 = 60. Then 60 × 0.90 = 54. The final price is $54. A common wrong answer, 80 × 0.65 = 52, applies both reductions to the original price.
Traps: adding percentages when they apply to different bases; mixing minutes and hours; averaging percentages without weighting; choosing the first series pattern that fits.