Quantitative Aptitude and Reasoning
Arithmetic rules worth drilling
- Learn percentage–fraction pairs (12.5% = 1/8, 16⅔% = 1/6, 20% = 1/5) to skip long division.
- Profit and loss: discount always applies to the marked price, profit to the cost price. Successive changes multiply: net = (1+a)(1+b) − 1.
- Time and work: take total work as the LCM of the days given, then add rates, never days.
- Average: new average = old average ± change ÷ number of items.
- SI = PRT/100; for two years CI − SI = P(r/100)².
- Mensuration: 1 acre = 8 kanal = 160 marla; 1 hectare ≈ 2.47 acre; 1 cubic metre = 1000 litres.
Reasoning patterns
Number series usually combine two rules (×2 + 3, squares ± 1); letter series shift by a fixed step, sometimes alternating direction. Coding-decoding is either a position shift or an alphabet reversal (A↔Z). Blood relations are solved by drawing one family tree and never assuming gender from a name. Direction sense ends with a Pythagoras step for the shortest distance.
Worked example
A trader marks goods 40% above cost and allows a 25% discount. Take cost = 100, so marked price = 140. Selling price = 140 × 0.75 = 105, giving a profit of 5 on 100, i.e. 5%. The whole question rests on the two different bases - discount on marked price, profit on cost.
Traps
- Applying the discount to cost instead of marked price.
- Adding percentage changes instead of multiplying them.
- Forgetting that in 'successive' discounts the second rate acts on the already-reduced value.
- In data-interpretation tables, treating a total row as another data row.