Quantitative Ability
Quantitative Ability tests numerical fluency and multi-step problem solving across arithmetic, algebra, geometry, mensuration, and data interpretation. The aim is accurate translation from words to equations, not calculation speed alone.
Core rules
- Define the variable and the unit before solving; write an equation for each condition.
- Percentage change = (new value − old value) / old value × 100. The base matters: profit percentage uses cost price; discount percentage uses marked price.
- Successive percentage changes multiply. Two 10% increases give 1.10 × 1.10 = 1.21, i.e. 21%, not 20%.
- For ratios, convert to parts or a common unit; for averages, total = average × count; weighted averages use the weights of each group.
- Average speed over equal distances is the harmonic mean 2xy/(x + y), not (x + y)/2.
- Geometry: use area, perimeter, Pythagoras, and mensuration formulas; draw a diagram and label given values.
Worked example
A shopkeeper marks an item 40% above cost and gives a 25% discount. Find profit percent. Let cost price = 100. Marked price = 140. Selling price = 140 × (1 − 0.25) = 105. Profit = 105 − 100 = 5. Profit percent = 5/100 × 100 = 5%. The discount is on the marked price, not on cost.
Traps
Adding successive discounts (10% + 10% = 20% is wrong; it is 19%); using selling price as the base for profit; mixing units such as km/h and m/s; assuming answers must be integers; forgetting that average speed is not the arithmetic mean when distances are equal.