Mathematics and Logical Reasoning
Core concepts
Expect arithmetic (percentages, ratios, proportions, averages), basic algebra (linear equations, simple systems), geometry (perimeters, areas, volumes, Pythagoras), unit conversions, and logical reasoning (series, analogies, syllogisms, coding-decoding). Speed and accuracy both matter.
Traps in questions
- Percentage direction: an increase of 20% followed by a decrease of 20% does not return to the starting value. Use multipliers: 1.20 × 0.80 = 0.96, a net loss of 4%.
- Unit mismatch: mixing metres and centimetres, or hours and minutes, in rate problems.
- Reading the question: "how much remains" versus "how much was removed".
- Series traps: alternating operations (×2, +3, ×2, +3) that look random if only the first differences are checked.
- Syllogism traps: conclusions that are plausible but not logically entailed by the premises.
Rule of thumb
For any percentage chain, convert to multipliers and multiply. For series, test differences first, then ratios, then alternating patterns. For syllogisms, draw the smallest possible diagram and ask whether a counter-example exists.
Worked example
A shop raises a price by 25%, then discounts it by 20%. Multipliers: 1.25 × 0.80 = 1.00. The final price equals the original, not a 5% increase.