Numeracy: Proportion, Percentage and Practical Data
What the Numeracy task tests
The GAT numeracy questions test everyday mathematical reasoning rather than formal algebra. Core concepts include percentages (increases, decreases, and reverse percentage), ratio and proportion (scaling recipes, maps, mixtures), rates (speed, wages per hour, cost per unit), unit conversion (length, mass, time, currency) and interpreting tables and graphs (reading axes, identifying misleading scales).
Traps to watch
- Percentage change from the wrong base. A price rising from $80 to $100 is a 25% increase, not 20%. Always divide the change by the original amount.
- Successive percentages. A 20% rise followed by a 20% fall does not return to the starting value; multiply factors (1.2 × 0.8 = 0.96).
- Reverse percentage. If a price after a 15% discount is $68, the original is 68 ÷ 0.85 = $80, not 68 × 1.15.
- Mismatched units. Convert minutes to hours or grams to kilograms before dividing.
- Graph scale distortion. Check whether an axis starts at zero; a truncated axis exaggerates differences.
Worked example
A recipe for 6 people needs 450 g of rice. How much for 10 people? Set up the proportion 450/6 = x/10, so x = 450 × 10 ÷ 6 = 750 g. Alternatively find the unit rate (75 g per person) and multiply by 10. The unit-rate method is safer when several ingredients must be scaled, because one calculation serves all of them.
When a question offers answer options, estimate first: round 450 to 500 and 6 to 5 to get roughly 100 g per person, confirming an answer near 750 g rather than 2700 g. Estimation catches inverted ratios, the most common error.