Module 2
パーセントの英語 （Pāsento no Eigo）
帰国子女・インターナショナルスクール生のための、デジタルSAT 数学の無料教材。独学で進められます。
Four small words decide the entire calculation:
0.20 × 50 = 10 （50の20%）50 × 0.80 = 40 （20%引き）× 1.20 （20%増加）Successive percents never add. Up 25% then down 20% is not "up 5%". Multiply the factors: 1.25 × 0.80 = 1.00 — exactly back where you started. Whenever a problem applies two percent changes in sequence, multiply; do not add.
日本語はこの区別を語ごと分けます。「20%引き」「20%増」「20%になる」は別々の三語で、取り違えようがありません。英語はこれを of / off / by / to の一語で区別します。どれも強く読まれず、読み飛ばしやすい語です。しかも of と off は一文字しか違いません。時間に追われていると、目はこの差を拾いません。パーセントの問題では、この一語を読むためだけに手を止めてください。
A jacket costs $80. The price is increased by 25%, and the new price is then decreased by 20%. What is the final price?
Correct Answer: B
Explanation: 80 × 1.25 = 100, then 100 × 0.80 = 80. The final price is $80 — identical to the start.
80 × 0.95). Percents do not add.80 + 20 − 16). The 20% decrease applies to $100, not $80.Rated Hard. Three of the four choices are what you get from a specific, reasonable-feeling misconception, and the correct answer looks suspicious because it equals the starting price.
A shirt is marked 30% off its original price of $45. What is the sale price?
Correct Answer: B
Explanation: "30% off" means you pay 70%. 45 × 0.70 = 31.50.
Rated Easy mathematically, but choice A is the answer to the question a hurried reader thinks was asked. Note that A is a perfectly correct calculation of the wrong quantity.
After increasing by 20%, the population of a town is 7,200. What was the population before the increase?
Correct Answer: B
Explanation: The 7,200 is after the increase, so 1.20 × (before) = 7200 → before = 7200 ÷ 1.20 = 6000. Check: 6000 × 1.2 = 7200. ✓
7200 × 0.80 — reversing a 20% increase by taking 20% off. Undoing a multiplication requires division, not the opposite percent.7200 × 1.20 — increasing again. The word "after" was missed, so the direction of time was reversed.Rated Hard. The whole question turns on the single word after, which establishes that 7,200 is the result rather than the starting point.