Module 1
逆転の罠 （Gyakuten no Wana）
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。
This is the highest-value module in the guide. A small set of English phrases reverse the order of the numbers as you write them:
| English | Correct | The trap |
|---|---|---|
| 5 less than x | x − 5 | 5 − x ✗ |
| 5 fewer than x | x − 5 | 5 − x ✗ |
| 5 subtracted from x | x − 5 | 5 − x ✗ |
| x subtracted from 5 | 5 − x | x − 5 ✗ |
| x divided into 20 | 20 ÷ x | x ÷ 20 ✗ |
Reference — the rest of the code. Everything that does not reverse (the full table is Module 3):
is/equals → = · a number → x · sum / more than / increased by → + · product / times / twice / of → × · quotient / per / divided by → ÷
Note that "less than" written in words behaves the opposite way to "less than" written as a symbol. "5 less than x" is x − 5, but "x is less than 5" is x < 5. Same two words, different job, decided entirely by sentence position.
日本語では「x より 5 小さい数」と言います。基準になる x が先に来て、直後のよりがそれを基準だと示し、引く量の 5 は後です。英語はこれが逆で、量が先、基準が後に来ます。日本語の語順のまま訳すと、毎回 5 − x と書いてしまいます。しかも出てきた数はそれらしく見えることが多く、間違いを知らせてくれるものが何もありません。less than や subtracted from を見たら、後ろに出てくる数を実際に手で先に書いてください。
Six less than twice a number is 10. What is the number?
Correct Answer: C
Explanation: "Six less than twice a number" → 2x − 6. So 2x − 6 = 10 → 2x = 16 → x = 8.
6 − 2x = 10 gives x = −2. If your answer to a word problem comes out negative when the context has no reason to be negative, suspect this first.(10 − 6) ÷ 2 — the 6 was subtracted again instead of added back.2 × (10 + 6) — multiplied where you should have divided.Rated Medium. The arithmetic is trivial; the difficulty is entirely in choice A, which is what the sentence says if you read it in Japanese word order.
When 4 is subtracted from a number, the result is 11. What is the number?
Correct Answer: C
Explanation: "4 is subtracted from a number" → x − 4. So x − 4 = 11 → x = 15.
4 − x = 11. The word "from" is what tells you which number is being reduced.11 − 4 — subtracted where you needed to add to undo.4 × 11; no multiplication appears anywhere in the sentence.Rated Easy because "from" is an explicit signpost. Learn to treat from as the marker that the following noun is the starting quantity.
A number is 9 less than 5 times another number n. Which expression represents the number?
Correct Answer: B
Explanation: "9 less than [5 times n]" — the whole quantity 5n is what gets reduced by 9. 5n − 9.
Rated Medium. Expression-form questions are harder than value questions because there is no numerical answer to sanity-check. The only defence is the mechanical rule.