Interchanges: swap “−” with “÷” and swap the digits 2 ↔ 6 everywhere. Which equality turns true?

Difficulty: Medium

Correct Answer: 32 - 16 ÷ 6 = 1

Explanation:


Introduction / Context:
Apply two systematic swaps: interchange “−” with “÷” in the expression and interchange the digits 2 and 6 wherever they appear. After both swaps, evaluate and find which option yields a true statement.


Given Data / Assumptions:

  • Operator swap: “−” ↔ “÷”.
  • Digit swap: 2 ↔ 6 globally.


Concept / Approach:
Transform each candidate fully (both sides) and compute. Standard precedence still applies after the swaps.


Step-by-Step Solution (Option C):

Original: 32 − 16 ÷ 6 = 1.After operator swap: 32 ÷ 16 − 6.After digit swap (2 ↔ 6): 36 ÷ 12 − 2.Evaluate: 36 ÷ 12 = 3; 3 − 2 = 1 → matches RHS (the RHS “1” is unchanged by 2/6 swap).


Verification / Alternative check:
Other options, after the same two swaps, produce decimal or mismatched values, so they are not true equalities.


Why Other Options Are Wrong:
They evaluate to numbers different from the right-hand side after performing both swaps.


Common Pitfalls:

  • Swapping only on the left and forgetting the right-hand side if it contains swappable digits.


Final Answer:
32 - 16 ÷ 6 = 1

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