Choose the correct statement after remapping: If “+” means “÷”, “×” means “+”, “−” means “×” and “÷” means “−”, which of the following becomes a true equation/inequality under the remapped meanings?
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A36 + 6 x 3 + 2 = 20
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B36 + 6 - 3 x 2 = 20
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C36 x 6 + 3 - 2 < 20
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D36 x 6 + 3 x 2 > 20
Answer
Correct Answer: 36 + 6 - 3 x 2 = 20
Explanation
Introduction / Context:This multiple-choice item asks you to evaluate four candidate statements after remapping each printed operator to a different arithmetic meaning. Your goal is to identify which option becomes a correct numerical relation (equality or inequality) under the new meanings.
Given Data / Assumptions:
- Operator mapping: “+” → “÷”, “×” → “+”, “−” → “×”, “÷” → “−”.
- Options include both equality “=” and inequalities “<”, “>”, which retain their usual meanings.
- Standard precedence applies after remapping.
Concept / Approach:Translate each option’s expression using the mapping, compute with precedence, and check the stated relation.
Step-by-Step Solution:Option B (candidate): 36 + 6 - 3 x 2 = 20.Remap: “+” → “÷”, “−” → “×”, “×” → “+”.Thus, 36 ÷ 6 × 3 + 2 = 20.Compute: 36 ÷ 6 = 6; 6 × 3 = 18; 18 + 2 = 20 ⇒ equality holds ✅Check one more for contrast: Option A → 36 ÷ 6 + 3 ÷ 2 = 20 ⇒ 6 + 1.5 = 7.5 ≠ 20.Options C and D also evaluate to values not satisfying their inequalities under the mapping (both LHS become large due to “×”→“+” and “+”→“÷” interplay).
Why Other Options Are Wrong:They produce numerical LHS values that do not satisfy the stated equality/inequality once remapped and evaluated with precedence.
Common Pitfalls:
- Forgetting to remap every occurrence of a symbol.
- Violating precedence by adding before completing all multiplications/divisions.
Final Answer:36 + 6 - 3 x 2 = 20 (Option B) becomes true under the given remap.