Mathematics / Quantitative Reasoning
This section tests arithmetic speed and a little algebra: percentages, ratio and proportion, average, profit and loss, simple and compound interest, time–work, time–speed–distance, area and perimeter, and number series. You have roughly a minute per item, so converting word problems into a single equation beats guesswork.
Core rules
- Percentage change = (change ÷ original) × 100; always divide by the original value.
- Profit% is on cost price unless stated otherwise; discount% is on marked price.
- Simple interest SI = P × R × T ÷ 100; Amount = P + SI.
- Compound interest: A = P(1 + R/100)^n.
- Average = sum ÷ count; if every item rises by k, the average rises by k.
- Work: if A finishes in x days, one day's work = 1/x; combined rate = 1/x + 1/y.
- Speed: distance = speed × time; convert km/h to m/s by multiplying by 5/18.
Worked example
"Two numbers are in the ratio 3 : 5. If 12 is added to each, the ratio becomes 5 : 7. Find the numbers." Let the numbers be 3x and 5x. Then (3x + 12)/(5x + 12) = 5/7. Cross-multiply: 21x + 84 = 25x + 60 → 24 = 4x → x = 6. The numbers are 18 and 30. Check: 30/42 = 5/7. ✔
Traps
- Dividing percentage change by the new value instead of the original.
- Adding percentages of profit and discount as if they cancel.
- Forgetting to convert units (cm to m, minutes to hours).
- In ratio problems, adding to the ratio instead of to the actual numbers.