Twelve speed-maths shortcuts worth memorising
Percentage change, successive discounts and ratio splitting — the shortcuts that save the most seconds.
Shortcuts buy attempts, not marks
A shortcut that saves 20 seconds is worthless if you never needed those seconds. Speed maths pays only on papers where you run out of time — which, for most aspirants, is every quant section. The twelve below are ranked by how often they actually appear, not by how clever they look.
Percentages and change
Learn the fraction equivalents cold: 12.5% is 1/8, 16.66% is 1/6, 37.5% is 3/8, 62.5% is 5/8, 87.5% is 7/8. Successive change of a% then b% is a + b + ab/100 in one line — never two steps. A discount followed by tax uses the same formula with signs.
Percentage-point vs percent-change confusion is a deliberate trap in data interpretation. If a value moves from 20% to 25%, that is 5 percentage points but a 25% increase. Circle which one the question asks before computing.
Ratios, averages and allegation
Ratio splitting: to divide 1170 in 2:3:4, add parts (9), divide once (130), multiply. One division total. Allegation answers every mixture question: place the two rates on the left, the mean in the middle, cross-subtract for the ratio — thirty seconds, every time.
Average speed over equal distances is the harmonic mean 2xy/(x+y), not the arithmetic mean. Average of first n natural numbers is (n+1)/2. These two lines cover a surprising share of arithmetic papers.
What to do this week
Write the twelve on one card. Drill 10 questions daily in speed mode using only the card — no long methods allowed. Time yourself; when the card feels slow, you have memorised it and can throw it away.
Practise it
Reading is not training
Every idea above is a drill inside UNLOCK — timed questions, instant solutions, and XP for doing it daily.
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Related notes
How to use a question timer without panicking
Timers only help if they train a decision rule. Here is the three-step rule we teach for a 30-second clock.
A decision tree for guessing under negative marking
Two options eliminated is not the same as three. A simple tree that keeps expected marks positive.
A repeatable framework for seating-arrangement puzzles
Stop drawing ten circles and hoping. Order the clues by constraint strength and the grid fills itself.