Operator re-mapping – identify which transformed equation is true: If "−" stands for "÷", "+" stands for "×", "÷" stands for "−" and "×" stands for "+", choose the correct statement.
Verbal Reasoning
Letter and Symbol Series
Difficulty: Medium
Choose an option
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A49 + 7 - 3 x 5 ÷ 8 = 20
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B49 - 7 + 3 ÷ 5 x 8 = 24
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C49 x 7 + 3 ÷ 5 - 8 = 16
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D49 ÷ 7 x 3 + 5 - 8 = 26
Answer
Correct Answer: 49 - 7 + 3 ÷ 5 x 8 = 24
Explanation
Introduction / Context:We must translate each candidate using the mapping and then evaluate using standard precedence. Only one option will reduce to a numerically correct equality.
Given Data / Assumptions:
- Mapping: "−" → "÷", "+" → "×", "÷" → "−", "×" → "+".
- Four candidate equalities to test.
Concept / Approach:Translate first, compute second. We check each option until one holds exactly.
Step-by-Step Solution:
Option B: "49 − 7 + 3 ÷ 5 × 8" translates to "49 ÷ 7 × 3 − 5 + 8".Evaluate left-to-right with precedence: 49 ÷ 7 = 7; 7 × 3 = 21; then 21 − 5 + 8 = 24. This matches the right-hand side 24.Other options, after translation, do not evaluate to the stated constants (they yield non-integers or mismatched totals).Verification / Alternative check:Re-run Option B's translation and arithmetic to confirm alignment with the mapping and precedence.
Why Other Options Are Wrong:
A/C/D reduce to incorrect numeric results once correctly translated, typically due to a hidden ×/÷ swap that changes magnitude substantially.Common Pitfalls:Ignoring precedence after translation or partially translating symbols and mixing meanings.
Final Answer:49 - 7 + 3 ÷ 5 x 8 = 24