If 'A' means '÷', 'B' means '×', 'C' means '+' and 'D' means '-', then which…
2025
If 'A' means '÷', 'B' means '×', 'C' means '+' and 'D' means '-', then which of the following will result in 22?
- A.
20 D 2 C 2 A 18 B 9
- B.
20 C 2 B 2 D 18 A 9
- C.
20 A 2 B 2 C 18 D 9
- D.
20 B 2 A 2 C 18 D 9
Attempted by 12 students.
Show answer & explanation
Correct answer: B
Concept: In letter-for-symbol coding questions, each letter is first replaced by its assigned mathematical sign, and the resulting numerical expression is then simplified using the standard order of operations (BODMAS): division and multiplication are carried out before addition and subtraction, working left to right at each level.
Substitute each letter with its sign and simplify every coded string using BODMAS:
Coded string | After substitution | Value |
|---|---|---|
20 D 2 C 2 A 18 B 9 | 20 − 2 + 2 ÷ 18 × 9 | 19 |
20 C 2 B 2 D 18 A 9 | 20 + 2 × 2 − 18 ÷ 9 | 22 |
20 A 2 B 2 C 18 D 9 | 20 ÷ 2 × 2 + 18 − 9 | 29 |
20 B 2 A 2 C 18 D 9 | 20 × 2 ÷ 2 + 18 − 9 | 29 |
Step-by-step for the string that equals 22:
Multiplication first: 2 × 2 = 4.
Division: 18 ÷ 9 = 2.
Left-to-right addition and subtraction: 20 + 4 − 2 = 22.
Cross-check: division and multiplication are applied before addition and subtraction in each of the other three strings as well — they settle at 19, 29 and 29, none of which equals 22, confirming that 20 + 2 × 2 − 18 ÷ 9 = 22 is the only string that satisfies the condition.