Swapped arithmetic symbols — Aptitude Question
Swapped arithmetic symbols: If '+' means '÷', '÷' means '−', '−' means '×' and '×' means '+', what is the value of:… Answer and worked solution on CodeKairo.
- Topic: Coding & Decoding
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 90 seconds
Question
If '+' means '÷', '÷' means '−', '−' means '×' and '×' means '+', what is the value of:
12 + 6 ÷ 3 − 2 × 8
Options
- 2
- 4
- 6
- 8
Show the answer and the worked solution
Correct answer: B. 4
Worked solution
- Substituting: 12 ÷ 6 − 3 × 2 + 8.
- Following BODMAS: 2 − 6 + 8.
- = 4.
Answer: 4.
The idea
Rewrite the whole expression before calculating anything, then apply the normal order of operations. Trying to substitute while computing is where errors come in.
Shortcut. Only two operations need BODMAS after rewriting: 12 ÷ 6 = 2 and 3 × 2 = 6. What remains, 2 − 6 + 8, is quickest regrouped as 2 + 8 − 6 = 4.
Common trap. "6" — working strictly left to right after substituting: 12 ÷ 6 = 2, 2 − 3 = −1, −1 × 2 = −2, −2 + 8 = 6; the multiplication 3 × 2 must come before the subtraction.