Mathematical Reasoning
What the section tests
Mathematical Reasoning tests school-level mathematics applied through word problems: algebra, ratios, geometry, sequences, counting and probability. The difficulty usually lies in translation, not computation.
Concepts you must command
- Algebraic translation: define a variable, write an equation for each stated relationship, solve, then confirm you answered the question asked.
- Ratios and mixtures: keep part-to-part and part-to-whole distinct; in mixtures, track the amount of the substance, not just the fraction.
- Work and rates: combine rates by adding reciprocals (1/a + 1/b = 1/t); average speed over equal distances is the harmonic mean.
- Geometry: area and perimeter formulas; similar figures scale lengths by k, areas by k², volumes by k³.
- Number properties: divisibility, primes, remainders, odd/even. Integer constraints can eliminate candidates quickly.
- Counting and probability: multiplication principle, combinations vs. permutations, P(not A) = 1 − P(A).
Traps
Misread qualifiers - at least, at most, exactly, consecutive, positive integer - change the answer set. Extraneous solutions appear after squaring or multiplying by an expression. Unit inconsistencies (minutes vs. hours) and answering the wrong quantity (solving for x when 2x + 1 is requested) are frequent. In probability, check whether draws are with or without replacement.
Rule of thumb
Estimate the answer before solving, then re-read the final question sentence to confirm the quantity and units match your result.
Worked example: two pipes fill a tank in 6 and 3 hours. Together: 1/6 + 1/3 = 1/6 + 2/6 = 1/2, so t = 2 hours - not the arithmetic mean of 4.5 hours.