Symbol swap — If ‘‘−’’ means ‘‘÷’’, ‘‘+’’ means ‘‘−’’, ‘‘÷’’ means ‘‘×’’, and ‘‘×’’ means ‘‘+’’, which equation becomes correct?
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A70 - 2 + 4 ÷ 5 x 6 = 44
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B70 - 2 + 4 ÷ 5 x 6 = 21
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C70 - 2 + 4 ÷ 5 x 6 = 341
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D70 - 2 + 4 ÷ 5 x 6 = 96
Answer
Correct Answer: 70 - 2 + 4 ÷ 5 x 6 = 21
Explanation
Introduction / Context:Each printed operator must be replaced by the designated real operator, after which we check which equality holds.
Given Data / Assumptions:
- Mapping: “−”→“÷”, “+”→“−”, “÷”→“×”, “×”→“+”.
- Standard arithmetic precedence applies.
Concept / Approach:Translate the left-hand side (LHS) using the mapping and evaluate; compare with the right-hand side (RHS) constant.
Step-by-Step Solution:LHS after mapping: 70 ÷ 2 − 4 × 5 + 6.Compute: 70 ÷ 2 = 35; 4 × 5 = 20; so LHS = 35 − 20 + 6 = 21.Hence the equality “= 21” is correct (Option B).
Verification / Alternative check:Evaluating other RHS values (44, 96, 341) does not match the computed LHS 21.
Why Other Options Are Wrong:They assert incorrect RHS values for the correctly decoded LHS.
Common Pitfalls:Replacing symbols but forgetting to keep normal precedence (× and ÷ before + and −).
Final Answer:Option B is correct.