Quantitative Reasoning and Mathematics
Quantitative reasoning and mathematics checks arithmetic fluency under time pressure, plus the ability to translate a short word problem into an equation and to read tables and charts. The mathematics is school-level - percentages, ratios, algebra, geometry, basic probability - but distractors are built around base errors and unit slips.
Core rules
- Percent change: (new − old)/old × 100. A rise from 80 to 100 is +25%, not +20%; the base is the original value.
- Percentage points vs percent: a rate moving from 4% to 5% rises 1 percentage point, or 25%.
- Successive changes multiply: +20% then −20% gives 1.2 × 0.8 = 0.96, a net −4%.
- Averages: total = average × count. A weighted average needs weights, not a simple mean of means.
- Ratios: keep units aligned and scale both parts by the same factor.
Worked example
A €250 jacket is raised by 20% and later discounted by 20%. What is the final price, and what is the net change? Raise: 250 × 1.20 = €300. Discount: 300 × 0.80 = €240. Net change: (240 − 250)/250 = −10/250 = −4%. The two 20% changes do not cancel because the second is taken on a larger base. Final price €240; net decrease 4%.
Data interpretation
Read axis labels and units before calculating; note whether a chart shows totals or shares; do not assume a line is linear between plotted points; check whether the question asks for a value, a difference, or a ratio.
Traps
Using the new value as the base; averaging percentages; mixing decimals and percentages; ignoring approximately; double-counting overlapping sets; and converting units after rather than before arithmetic.