Quantitative Reasoning and Data Interpretation
What to master
Percentages (successive change, reverse percentages), ratios and proportions, averages and weighted averages, rates (work and distance), and basic probability. For data interpretation, know how to read tables, bar/line charts, and pie charts, and how to compute totals, shares, and percent differences from them.
Traps that appear
- Successive percentages: a 20% rise then a 20% fall does not return to the start. Use multipliers: 1.20 × 0.80 = 0.96, a 4% net loss.
- Reverse percentages: if a price after a 25% discount is 90, the original is 90 ÷ 0.75 = 120, not 90 × 1.25.
- Averages of averages: never average two group means unless the groups are the same size; use weighted averages.
- Units in charts: check whether figures are in thousands or millions before comparing.
- Percent of what base? "Percent more than" and "percent of" differ; identify the base value each time.
Rule of thumb
For any percent-change chain, convert each change to a multiplier (increase: 1 + r; decrease: 1 − r), multiply them, then convert back. For data questions, write down the exact quantity asked for before touching the numbers, and estimate first so you can spot an answer that is off by a factor of ten.
Worked example
A town's population rises 10% one year and falls 10% the next. Net change = 1.10 × 0.90 = 0.99, so it ends 1% below where it started - not unchanged.