Numerical Reasoning
Numerical Reasoning checks fluency with number series, percentages, ratio and proportion, averages, time and work, time, speed and distance, and simplification. The exam rewards disciplined setup over mental arithmetic speed.
Core rules
- Percentage change = change divided by the original value, times 100. The denominator is always the base before the change.
- Successive changes multiply: two successive 10% increases give 1.1 x 1.1 = 1.21, that is 21%, not 20%.
- Average = total divided by count; merging groups requires weighting by group size.
- A ratio a : b means quantities ax and bx; convert to fractions of the total before sharing.
- Work problems combine rates (1/a + 1/b), never times.
Worked example
A shirt marked 800 is discounted 25%, then a further 10% on the reduced price. What is the final price?
After the first discount: 800 x 0.75 = 600. The second discount applies to 600, not 800: 600 x 0.90 = 540. The equivalent single discount is 30%, not 35%, because the second 10% is taken on a smaller base.
Series technique
Check first differences, then second differences; check ratios between consecutive terms; then test alternating patterns in which odd and even positions follow separate rules.
Traps
- Treating successive percentage changes as additive.
- Using the new value as the base for a percentage decrease.
- Mixing units: km/h with metres, minutes with hours.
- Averaging two averages without weighting for group size.
- Reading a series as one pattern when it is two interleaved series.
- Answering the wrong quantity: the question asks for the discount, not the final price.