Quantitative Methods
Quantitative Methods tests numerical fluency for administrative decisions: ratios, percentages, averages, rates, work and motion problems, sets, and basic probability. The aim is accurate setup and unit control, not advanced mathematics.
Core rules
- Percentage change = (new − old) / old × 100; percentage points measure absolute difference between percentages.
- Weighted average = sum of (value × weight) / sum of weights.
- For work rates, add rates for joint work: 1/T = 1/A + 1/B; do not average completion times.
- For speed, distance = speed × time; average speed for equal distances is the harmonic mean, not the arithmetic mean.
- In sets, |A ∪ B| = |A| + |B| − |A ∩ B|.
Worked example
A can complete a file review in 12 days; B takes 18 days. Together, their rate is 1/12 + 1/18 = 3/36 + 2/36 = 5/36 files per day. Time = 36/5 = 7.2 days. If A works alone for 3 days, A completes 3/12 = 1/4 of the work; remaining 3/4 at joint rate takes (3/4) ÷ (5/36) = 27/5 = 5.4 days, total 8.4 days.
Traps
Do not add times for joint work. Do not confuse percent and percentage points. Do not use the original base after a change without updating it. Do not ignore units or rounding. Do not average speeds over equal distances arithmetically.