Mathematics and Reasoning
What this domain tests
Mathematics and Reasoning tests numerical fluency, algebraic manipulation, geometry, data interpretation and logical puzzles. Speed matters, but method matters more: most errors are setup errors, not calculation errors.
Core rules
- Percentage: always identify the base. A 25% markup on cost and a 10% discount are applied to different bases.
- Ratio and proportion: convert to a common unit before forming ratios; use the unitary method for work and pipes.
- Averages: total = average × number; adding a value shifts the average toward that value.
- Algebra: isolate the variable, factorise, and check by substitution.
- Geometry: memorise area and volume formulas and Pythagoras; draw a diagram before computing.
- Reasoning: in series, check differences, ratios, squares, cubes and alternating patterns; in syllogisms, draw Venn diagrams and do not convert 'some' into 'all'.
Worked example
A trader marks an item 25% above cost and allows a 10% discount. Find profit percent. Let cost = 100. Marked price = 125. Discount = 10% of 125 = 12.5. Selling price = 112.5. Profit = 12.5 on cost 100, so profit = 12.5%. Trap: adding 25% and subtracting 10% gives 15%, which is wrong because the discount base is the marked price.
Traps
Successive percentage changes do not add; use multipliers such as 1.25 × 0.90. In time-and-work, add rates, not times. In reasoning, do not assume real-world truth in syllogisms; follow only the stated premises.