Quantitative Reasoning and Numerical Ability
Quantitative Reasoning and Numerical Ability tests arithmetic, percentages, ratios, rates, averages, data interpretation and basic statistics. The emphasis is on correct setup and unit control under time pressure, not advanced mathematics.
Core rules
- Percentage change = (new − old) ÷ old × 100%. Percentage points describe a difference between two percentages; percent describes a relative change.
- Reverse percentage: if a price after a 20% increase is $120, the original is $120 ÷ 1.2 = $100, not $96.
- Ratios must share the same unit before combining. If a ratio is 3:5 and the total is 40, one part is 40 ÷ 8 = 5.
- Weighted average = sum of all values ÷ total number of cases. Do not average two group averages unless the groups are the same size.
- Mean is affected by outliers; median is the middle value after ordering; mode is the most frequent value; range = highest − lowest.
Data interpretation
Read the title, units, axes, base year and footnotes before calculating. Check whether a chart shows counts, rates or percentages. A fall from 50% to 40% is a 10-percentage-point fall but a 20% relative fall.
Worked example
A crime-prevention budget rises from $2.4 million to $3.0 million. What is the percentage increase? Difference = $0.6 million. Divide by the original: 0.6 ÷ 2.4 = 0.25, so the increase is 25%. The trap is to divide by the new figure, 0.6 ÷ 3.0 = 20%, which answers a different question: the increase as a percentage of the new budget. Always identify the base named in the question.
Statistics example
Response times in minutes: 8, 10, 10, 12, 15. Mean = 55 ÷ 5 = 11; median = 10; mode = 10; range = 7. If one unusually slow case of 60 is added, the mean rises sharply but the median changes little, so the median better represents a typical case.
Traps that cost marks
- Mixing percent and percentage points.
- Using the new value as the denominator for a percentage increase.
- Ignoring units such as minutes versus hours, or thousands versus millions.
- Treating an unweighted average of group averages as the overall average.
- Forgetting to order data before finding the median.
- Reading a graph's visual height without checking the scale.