Choose the modification (swap specified operator pair and interchange the indicated digits) that makes (3 ÷ 4) + 2 = 2 a true statement

Difficulty: Medium

Correct Answer: + and ÷, 2 and 3

Explanation:


Introduction / Context:
We must select a combined transformation—swapping the roles of two operators and interchanging two digits—so that the given equality becomes correct. Such questions assess attention to precedence and careful, serial application of multiple edits.


Given Data / Assumptions:

  • Initial statement: (3 ÷ 4) + 2 = 2 (false).
  • Each option specifies (i) a pair of operators to swap globally and (ii) a pair of digits to interchange in the LHS.
  • Standard precedence applies after edits.


Concept / Approach:
Process the LHS in two stages: perform the operator swap, then interchange the digits wherever they occur. Finally, evaluate and compare to 2.


Step-by-Step Solution:
Try Option C: swap “+” and “÷”; interchange digits 2 and 3.Operator swap first: (3 + 4) ÷ 2.Now interchange 2 ↔ 3 in the LHS: (2 + 4) ÷ 3.Evaluate: (2 + 4) ÷ 3 = 6 ÷ 3 = 2, which matches the RHS.


Verification / Alternative check:
Other options fail: e.g., Option A leads to (3 + 4) ÷ 2 = 3.5 (before digit swap) and still does not reach 2 after its swap; Option B introduces a minus that moves the value away from the target.


Why Other Options Are Wrong:
They yield values ≠ 2 due to either excessive increase (addition) or a detrimental subtraction.


Common Pitfalls:
Applying the digit swap before the operator swap or neglecting the parentheses in evaluation.


Final Answer:
+ and ÷, 2 and 3 makes the equation true.

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