Why +10% then −10% isn't 0% on SAT Math
A price goes up 10%, then down 10%. If you answered "back to the original", you hit the single most common percent trap on the SAT.
Why it happens
Percent changes feel like ordinary numbers, so your brain wants to add them. But each change applies to a *different base* — the second 10% is taken from a bigger number than the first.
See the trap
A $200 jacket is marked up 10%, then discounted 10%. Final price?
+10% − 10% = 0% → $200.
200 × 1.10 × 0.90 = $198. The net change is −1%, not 0%.
How to actually fix it
- 1Convert every percent change to a multiplier (×1.10, ×0.90).
- 2Multiply the multipliers — never add the percents.
- 3Write the intermediate value after each change.
Practice this trap · 3 real questions
Each of these is a question from the free bank that turns on the mistake above — the trap is the reason its wrong answer looks right. Easiest first.
FAQ
Does the order of the changes matter?
No — multiplication commutes. Up 10% then down 10% equals down 10% then up 10%: both give ×0.99.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.
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