Which transformed equation is correct? Mapping: “+” = ×, “−” = ÷, “×” = +, “÷” = −
Verbal Reasoning
Mathematical Operations
Difficulty: Medium
Choose an option
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A18 ÷ 6 + 4 - 2 ÷ 3 = 22
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B18 + 6 - 4 x 2 ÷ 3 = 26
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C18 x 6 - 4 + 7 x 8 = 47
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D18 - 6 x 7 ÷ 2 + 8 = 63
Answer
Correct Answer: 18 + 6 - 4 x 2 ÷ 3 = 26
Explanation
Introduction / Context:Each operator in the printed equation stands for a different actual operation. Determine which full equation remains true once all symbols are remapped and then evaluated with standard precedence.
Given Data / Assumptions:Mapping: + → ×, − → ÷, × → +, ÷ → −.
Concept / Approach:Remap an option and evaluate carefully. If LHS equals RHS, that option is correct.
Step-by-Step Solution (Option B):
Original: 18 + 6 − 4 × 2 ÷ 3 = 26.After mapping: 18 × 6 ÷ 4 + 2 − 3.Compute ×/÷: 18 × 6 = 108; 108 ÷ 4 = 27.Then +/−: 27 + 2 − 3 = 26 → matches RHS.Verification / Alternative check:Checking the other options shows mismatches (e.g., Option A maps to 21, not 22).
Why Other Options Are Wrong:After mapping, their left sides do not equal the right sides.
Common Pitfalls:
- Changing precedence according to the original symbols instead of the mapped operations.
Final Answer:18 + 6 - 4 x 2 ÷ 3 = 26