Interchange one pair of signs to make the equation true: 16 − 21 ÷ 7 × 6 + 3 = 31
Verbal Reasoning
Mathematical Operations
Difficulty: Medium
Choose an option
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A- and +
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B+ and x
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C÷ and +
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D÷ and x
Answer
Correct Answer: + and x
Explanation
Introduction / Context:Choose a global swap of one pair of operators so the equality holds.
Given Data / Assumptions:
- Original: 16 − 21 ÷ 7 × 6 + 3.
- Target: 31.
Concept / Approach:Try each swap and evaluate with precedence.
Step-by-Step Solution:Swap “+” and “×” (Option B): 16 − 21 ÷ 7 + 6 × 3.Compute: 21 ÷ 7 = 3; so 16 − 3 + (6 × 3 = 18) = 31 ✔.
Verification / Alternative check:Other options give results like 9, −5.5, etc., not 31.
Why Other Options Are Wrong:They fail to compensate the large middle product/division segment to hit 31.
Common Pitfalls:Applying the swap to only one occurrence or changing evaluation order.
Final Answer:+ and x.