Numerical Reasoning and Quantitative Aptitude
Numerical reasoning and quantitative aptitude tests your ability to solve arithmetic and data-interpretation problems accurately under time pressure. Expect percentages, ratios, averages, rates, simple and compound interest, and questions based on tables, charts or short word problems.
Core rules
- Percentage change=(new−old)÷old×100. A rise from 80 to 100 is a 25% increase, not 20%.
- Percentage points: 12% to 15% is 3 points but a 25% relative rise.
- Ratios: convert to a common unit first; total parts=sum of terms. If a:b=c:d, then ad=bc. In ratio word problems, fix the base quantity and keep units aligned.
- Weighted average=(n₁x₁+n₂x₂)÷(n₁+n₂), not the simple mean of averages.
- Work rate: times a and b give combined rate 1/a+1/b. Average speed=total distance÷total time, not the mean of two speeds.
- Simple interest=P×r×t; compound A=P(1+r/n)^(nt).
- To compare fractions, cross-multiply or convert to decimals.
Data interpretation
Read the title, units and axis labels before calculating. Note whether the chart starts at zero. Use estimation to eliminate options, but calculate precisely once two options are close. When a table gives values in thousands, multiply by 1,000 before comparing with a total in millions. For pie charts, the whole is 360° or 100%; label each sector's share before computing differences.
Worked example
A department spent 2.4 million last year. Staff costs were 35%, operations 25%, and the rest capital. What was capital spending? Reasoning: capital share=100%−35%−25%=40%. 40% of 2.4m=0.4×2,400,000=960,000. Check: staff 840,000; operations 600,000; total 1,440,000; capital 960,000. The three parts sum to 2.4m, so the answer is consistent.
Traps that cost marks
- Adding percentage changes instead of compounding them (a 10% rise then a 10% fall does not return to the start).
- Using the wrong base for a percentage increase or decrease.
- Averaging percentages without weighting by group size.
- Misreading "per 1,000" or "per capita" figures as totals.
- Rounding intermediate values too early, which shifts the final option.
- Confusing "times more than" with "times as many as".