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If in a code language, If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’ and ‘D’ stands for ‘−’, then the resultant of which of the following would be 55?
16 D 112 A 63 C 77 B 31
16 A 112 B 63 C 77 D 31
16 B 112 C 63 A 77 D 31
16 C 112 D 63 A 77 B 31
16 A 112 B 63 C 77 D 31
Substitute the symbols with their mathematical operators (A=÷, B=×, C=+, D=−) and apply the BODMAS rule. Check options starting from the official correct option to verify quickly.
Substitute the symbols with their mathematical operators (A=÷, B=×, C=+, D=−) and apply the BODMAS rule. Check options starting from the official correct option to verify quickly.
Step 1: Understand the Symbol Replacements
Replace the given letters with their mathematical equivalents: 'A' becomes division (÷), 'B' becomes multiplication (×), 'C' becomes addition (+), and 'D' becomes subtraction (−).
Step 2: Test Option B Expression
Substitute symbols into Option B: 16 A 112 B 63 C 77 D 31 becomes 16 ÷ 112 × 63 + 77 − 31.
Step 3: Apply BODMAS Rule
First, perform division and multiplication from left to right: (16 / 112) = 1 / 7. Next, multiply by 63: (1 / 7) × 63 = 9.
Step 4: Perform Addition and Subtraction
Substitute back into the expression: 9 + 77 − 31. Add 9 and 77 to get 86, then subtract 31 to get 86 − 31 = 55, which matches the target.
A: Yields a non-matching fractional or incorrect arithmetic result. C: Yields a different numerical value upon evaluation. D: Yields an incorrect arithmetic value different from 55.
B is correct because replacing the letters with their respective arithmetic operators in Option B (16 ÷ 112 × 63 + 77 - 31) and applying BODMAS evaluates precisely to 55.
Always follow strict BODMAS/PEMDAS order when evaluating coded mathematical expressions to avoid calculation errors.
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