General Mathematics and Mental Ability
Core concepts
Arithmetic: percentage, profit–loss, ratio, average, simple and compound interest, partnership. Algebra: linear equations, quadratic factorization, exponents. Geometry: triangles, circles, area and perimeter. Mental ability: number series, analogy, coding–decoding, direction sense, blood relations, and logical syllogism.
Traps to expect
- Percentage base confusion: "A is 20% more than B" means A = 1.2B, not B = 0.8A. Always fix the base.
- Successive percentage change: two changes of +10% and −10% give a net −1%, not 0%.
- Profit–loss on different bases: profit% is on cost price; discount% is on marked price.
- Series traps: alternating operations (+3, ×2, +5, ×2) rather than a single rule.
- Direction sense: track net displacement with a rough sketch; turns are relative to the facing direction, not fixed compass points.
Rule of thumb
For successive percentage changes use the multiplier form: final = original × (1 ± a)(1 ± b). This avoids sign errors and works for interest, discount, and population problems alike.
Worked example
A shopkeeper marks an item 40% above cost and gives a 25% discount. What is the profit percent? Let cost = 100. Marked price = 140. Discount = 25% of 140 = 35. Selling price = 105. Profit = 5 on cost 100, so profit = 5%. Multiplier shortcut: 100 × 1.40 × 0.75 = 105 → 5% profit. The trap is computing 25% of cost instead of marked price.