If ‘A’ means ‘+’, ‘B’ means ‘−’, ‘C’ means ‘×’ and ‘D’ means ‘÷’, then which…
2021
If ‘A’ means ‘+’, ‘B’ means ‘−’, ‘C’ means ‘×’ and ‘D’ means ‘÷’, then which of the following equation is correct?
- A.
9A16D64C32B3 = 14
- B.
26D14C7A9B3 = 20
- C.
8A15D5C11B7 = 35
- D.
6C21D7A9B15 = 10
Attempted by 28 students.
Show answer & explanation
Correct answer: A
Concept
In a symbol-substitution problem, first replace each coded letter with the arithmetic operator it stands for, then evaluate the resulting expression using the BODMAS / order-of-operations rule: division and multiplication are performed before addition and subtraction, working left to right within each tier. The substitution given is A = +, B = -, C = ×, D = ÷.
Application
Decode the expression 9A16D64C32B3 by replacing the letters: it becomes 9 + 16 ÷ 64 × 32 - 3. Now apply BODMAS in order:
Division first: 16 ÷ 64 = 0.25, giving 9 + 0.25 × 32 - 3.
Then multiplication: 0.25 × 32 = 8, giving 9 + 8 - 3.
Finally addition and subtraction, left to right: 9 + 8 = 17, then 17 - 3 = 14.
The decoded expression equals 14, which is exactly the value stated on its right-hand side, so this equation is the correct one.
Cross-check
Test the others the same way and each fails: 26 ÷ 14 × 7 + 9 - 3 = 19 (stated 20); 8 + 15 ÷ 5 × 11 - 7 = 34 (stated 35); and 6 × 21 ÷ 7 + 9 - 15 = 12 (stated 10). Only the expression evaluating to 14 has a left-hand side that genuinely matches its right-hand side.