Module 2
Percent Language.
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:
- 20% of 50 →
0.20 × 50 = 10（50の20%） - 20% off 50 →
50 × 0.80 = 40（20%引き） - increased by 20% →
× 1.20（20%増加） - increased to 20% → the new value is 20% （20%になる）
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.
日本人がハマる理由
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。
練習問題
難易度は出題者による目安です。College Board の判定ではありません。
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.
- (A) $76: From treating the net change as −5% (
80 × 0.95). Percents do not add. - (C) $84: From treating the net change as +5%, or from taking both percents of the original $80 (
80 + 20 − 16). The 20% decrease applies to $100, not $80. - (D) $100: The price after the first step only. The second sentence was not applied.
Difficulty Justification
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.
- (A) $13.50: This is 30% of $45 — the size of the discount, not the price you pay. The classic of/off confusion.
- (C) $45.00: The original price, unchanged.
- (D) $58.50: The price increased by 30%. "Off" was read as "on".
Difficulty Justification
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. ✓
- (A) 5,760: From
7200 × 0.80— reversing a 20% increase by taking 20% off. Undoing a multiplication requires division, not the opposite percent. - (C) 7,180: From subtracting 20 rather than 20%. The percent sign was dropped.
- (D) 8,640: From
7200 × 1.20— increasing again. The word "after" was missed, so the direction of time was reversed.
Difficulty Justification
Rated Hard. The whole question turns on the single word after, which establishes that 7,200 is the result rather than the starting point.