Interchanges: swap “+” with “×” and swap the digits 3 ↔ 7 everywhere. Which statement becomes correct after performing both swaps?

Difficulty: Medium

Correct Answer: 23 + 17 x 73 = 388

Explanation:


Introduction / Context:
This is a two-layer transformation puzzle. First interchange the operators “+” and “×”. Second, replace every digit 3 with 7 and every digit 7 with 3 anywhere they occur (on both sides). After applying both swaps, check which equality holds numerically.


Given Data / Assumptions:

  • Operator swap: “+” ↔ “×”.
  • Digit swap: 3 ↔ 7 in every number (e.g., 23 → 27, 17 → 13, 73 → 37).


Concept / Approach:
Transform each option entirely (LHS and RHS), then evaluate the transformed LHS to see whether it equals the transformed RHS.


Step-by-Step Solution:

Consider Option D: 23 + 17 × 73 = 388.After operator swap → 23 × 17 + 73; after digit swap → 27 × 13 + 37.Compute: 27 × 13 = 351; 351 + 37 = 388.RHS “388” has no 3/7 digits, so remains 388. Equality holds → Option D is correct.


Verification / Alternative check:
Quick checks on other options show mismatches after the two-step swap (e.g., Option A transforms to 27 × 13 + 37 = 388 on LHS but compares with 1241, which does not match).


Why Other Options Are Wrong:

  • Their transformed LHS and RHS evaluate to different numbers.


Common Pitfalls:

  • Forgetting to swap digits on the RHS as well.
  • Applying swaps in the wrong order; here either order still leaves Option D the only true equality.


Final Answer:
23 + 17 x 73 = 388

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