Mathematics and Quantitative Reasoning
Core concepts
Quantitative reasoning covers arithmetic (fractions, decimals, percentages, ratio and proportion), averages, profit and loss, simple and compound interest, time-speed-distance, time and work, mensuration, basic algebra, number series, data interpretation, and elementary probability. Strong candidates convert word problems into equations, keep units consistent, and use estimation to sanity-check answers.
Traps
Frequent traps include mixing percentage points with percent change, applying successive discounts additively, averaging speeds arithmetically instead of using total distance over total time, forgetting unit conversions (minutes to hours, centimetres to metres), counting inclusively in calendar or page-number questions, and reversing cost price and selling price. Data interpretation questions often hide a change in base year or a switch from absolute numbers to percentages.
Worked example
A shirt is discounted by 20% and then by a further 10%. What is the total discount? After the first discount, the price is 80% of the original. The second discount applies to that reduced price: 80% × 90% = 72%, so the customer pays 72% and receives a 28% discount, not 30%. Additive discounting overstates the reduction.
Rule of thumb
Translate percentages to fractions, write the base for every comparison, and check whether the answer is plausible in size and units. When two changes occur in sequence, multiply the multipliers rather than adding the percentages.