Using the wrong base in percentage change
Percentage change is always measured against the ORIGINAL value: (new − old) ÷ old. Dividing by the new value — or by the total, or by an average — gives a plausible-looking number that's simply wrong.
Why your brain does this
After computing the difference, your attention is on the most recent number you touched — usually the new value — so it feels natural to divide by it. Test writers know this and put the inverted answer among the options every time.
The fix
Before dividing, say (or write) which number is the base: "change FROM 2023" means 2023 is the base. If the question says "from A to B", A is the base — no exceptions. Sanity check: a rise from 100 to 150 must be +50%, not +33%.
See the trap in a real question
| Year | Revenue (£m) |
|---|---|
| 2023 | 620 |
| 2024 | 760 |
By what percentage did Carraway plc's Revenue change from 2023 to 2024?
Percentage change = (new − old) ÷ old × 100. Always divide by the original (earlier) value. The correct answer is 22.6%. Traps to avoid: 20.3% comes from the "base as average" error; 10.1% comes from the "wrong base total" error; 122.6% comes from the "ratio not change" error; 18.4% comes from the "inverted base" error.
Where it strikes
This trap appears in 42 of our questions, across: Percentage change · Margin change.
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