Numerical Reasoning and Quantitative Analysis
Numerical Reasoning and Quantitative Analysis tests arithmetic accuracy under time pressure: percentages, ratios, averages, rates, series and short word problems framed in budget, staffing and demographic terms.
Core rules
- Percentage change = (new − old) ÷ old × 100. The base is whatever the change is measured against, and it changes between steps.
- Successive changes multiply; they never add. Two changes of +25% and −20% give a factor of 1.25 × 0.80 = 1.00.
- Distinguish percentage points from percent. A share rising from 20% to 24% is +4 percentage points but +20 percent.
- Work-rate problems are reciprocal: combined time = 1 ÷ (1/a + 1/b).
- Averages: a weighted mean is required when group sizes differ; for equal distances at two speeds, average speed is the harmonic mean, not the arithmetic mean.
- Number series: check differences, then ratios, then alternating or two-interleaved sequences before assuming a polynomial rule.
Worked example
A uniform allowance of 800 is raised by 25% and then a 20% discount is applied to the new figure during procurement. Final cost = 800 × 1.25 = 1,000; then 1,000 × 0.80 = 800. The two changes cancel exactly. The common error is to net +25% and −20% as +5% and answer 840.
Traps
Applying a percentage to the wrong base; averaging two averages; forgetting that a discount after a markup never restores the original unless the factors are reciprocal; and answering the intermediate value when the question asks for the total or the difference.