Quantitative Reasoning: Arithmetic Under Time Pressure
Choosing the operation fast
Quantitative items are mostly one- or two-step arithmetic dressed in words: percentages, ratios and proportions, averages, fractions and decimals, order of operations, rate–time–distance, and number series. The arithmetic is rarely hard; the difficulty is selecting the right operation quickly.
Know these relationships cold: part = percent × whole; percent change = (new − old) ÷ old; average = sum ÷ count, so sum = average × count; and rate × time = distance. For number series, check differences first, then ratios, then alternating patterns (two interleaved sequences), then squares or cubes plus or minus a constant.
Traps. (1) Percent of versus percent increase - "20% more than 50" is 60, not 70. (2) Unit mismatch, such as minutes inside an hours problem or cents inside a dollars answer. (3) Averaging two averages when the group sizes differ. (4) Answer choices that are intermediate results rather than the requested value. (5) Reading "how many more" as "how many."
Estimation is a strategy. Because choices are usually spaced apart, round aggressively, compute, and take the nearest option - but verify whenever two choices are close together.
Worked example. A jacket is marked down 25%, then the sale price is marked down another 20%. What single discount is equivalent? Start at 100 → 75 → 60, so the final price is 60% of the original, a 40% discount, not 45%. Adding the two percentages is the classic error; successive percent changes compound.
Rule of thumb: before computing, label each number in a word problem with its unit and write down exactly what the question asks for.