Every formula the tests actually use — there are fewer than thirty. Each one comes with its classic trap, because in numerical reasoning the formula is rarely the problem; applying it to the wrong base is. Bookmark this page; revising it the night before is a legitimate strategy.
part = rate% × wholeTrap: "% of" multiplies — it never divides.
change% = (new − old) ÷ old × 100Trap: The base is always the OLD value — using the new value is the most common mistake in the entire test.
original = final ÷ (1 ± rate)Trap: After a 12% rise, divide by 1.12 — never subtract 12% from the final.
total = (1 ± r₁)(1 ± r₂) − 1Trap: +10% then −10% is −1%, not 0 — percentages never simply add.
pp = simple difference of two ratesTrap: From 20% to 25% is +5pp but +25% relative.
share = total × part ÷ (sum of parts)Trap: Divide by the sum of ALL parts (1:2:5 → ÷8), not by the largest part.
a/b = c/x → x = b·c ÷ aTrap: Cross-multiply once; don't chain operations.
new = old × (new basis ÷ old basis)Trap: Check whether the quantity scales up or down before multiplying.
mean = sum ÷ countmean = Σ(value × weight) ÷ Σ(weights)Trap: Group sizes are the weights — averaging two group means equally is wrong unless the groups are equal.
missing = mean × count − sum(known)(n₁m₁ + n₂m₂) ÷ (n₁ + n₂)speed = distance ÷ time (cover the one you want)Trap: Minutes must become hours before mixing with mph — 90 min = 1.5 h, not 0.9.
rate = output ÷ inputamount × rate (to foreign) · amount ÷ rate (back)Trap: Check which direction the quoted rate goes before multiplying.
per head = total ÷ populationinterest = principal × rate × yearsfinal = principal × (1 + rate)ʸᵉᵃʳˢTrap: Compound multiplies each year — simple-interest shortcuts undershoot.
gross = net × (1 + rate); net = gross ÷ (1 + rate)units = fixed costs ÷ (price − variable cost)margin = profit ÷ price · markup = profit ÷ costTrap: Same profit, different base — a 25% markup is a 20% margin.
value = base value × index ÷ 100P = favourable ÷ totalP(not A) = 1 − P(A)P(A and B) = P(A) × P(B)Trap: Multiply for AND (both), add for OR (either, minus overlap).
either = A + B − bothThe tests measure whether you apply these fast, on unfamiliar data, under a clock. Ten minutes of practice tells you which of these you only think you know.
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