Percentages & Percentage Change — the first numerical drill every Pro member starts with, exactly as it teaches in the product: a short lesson, real test-style questions, and a named diagnosis of the specific mistake behind every wrong answer.
Step 1 · The three-minute lesson
A calculator is on the desk in every test we cover, so the skill is never the arithmetic — it is choosing the right two numbers and dividing them the right way round. Five ideas cover almost every percentage question you will ever be asked.
Every percentage question is really asking one thing: percentage of what? That denominator — the base — is where nearly all the marks are lost.
Percentage change = (change ÷ original) × 100. The base is always the ORIGINAL (earlier) value — never the new one.
Percentage points is an absolute gap: subtract. Per cent is a relative change: divide by the original.
A tax rate rises from 5% to 7%. The percentage-point change is 7 − 5 = 2 pp (just subtract). The percentage change is 2 ÷ 5 = 0.4 = 40% (divide by the original, 5). Same move, two correct answers — the units the question asks for tell you which.
Turn every change into a multiplier and you replace two steps with one keystroke: +15% is × 1.15, −15% is × 0.85. A rise adds to 1; a fall subtracts from 1.
A £200 price after a 15% rise is 200 × 1.15 = £230 in one pass — no working out the £30 and adding it back on.
If the figure you are given comes after the change, you divide by the multiplier to get back — you never apply the percentage forwards.
'£4,560 including 20% VAT' means ÷ 1.2, never × 0.8. The net is 4,560 ÷ 1.2 = £3,800; check 3,800 × 1.2 = 4,560. Why not × 0.8? Because 0.8 × 1.2 = 0.96, not 1 — only ÷ 1.2 undoes × 1.2.
Two changes over two periods act on different bases, so they never add — they chain. −15% then +15% is × 0.85 × 1.15 = 0.9775: a 2.25% fall, not zero.
Equal-and-opposite changes always leave you slightly below the start. A 20% rise then a 20% fall is × 1.2 × 0.8 = 0.96 — a 4% fall.
Step 2 · Six questions
Six questions from the drill, warm-up to challenge. Answer each one and the specific mistake behind your choice — not a generic "incorrect" — is diagnosed on the spot. That diagnosis loop is what the whole product does, across 25 drills and 87 named failure modes.
The trap, named
This is 1 of the 87 named failure modes the full programme trains against.
The method
Take away:
Drill complete
/6
Traps that caught you
15 minutes, one attempt, instant estimated percentile. No card required.
See what the full programme looks like inside →Untimed by default — this page teaches. In the real programme, every drill ends with a beat-the-clock unit at test pace.
Start where every member starts: the free 15-minute Benchmark. It scores you against the field and shows which categories — and which traps — need the work.
Start Free Benchmark