If 2 is added to each even digit and 2 is subtracted from each odd digit in the number 5973642, then what will be the sum of all…

Question

If 2 is added to each even digit and 2 is subtracted from each odd digit in the number 5973642, then what will be the sum of all the even digits in the new number thus formed?

1. A. 24
2. B. 20
3. C. 16
4. D. 18 (Correct answer)

Correct Answer

Option D — 18

Detailed Solution & Explanation

The correct answer is 18.

Key Points

• Apply the rule digit by digit to 5973642 — add 2 to each even digit, subtract 2 from each odd digit:
  • 5 (odd) → 3, 9 (odd) → 7, 7 (odd) → 5, 3 (odd) → 1
  • 6 (even) → 8, 4 (even) → 6, 2 (even) → 4
• The new number is 3751864.
• Now identify the even digits in the new number: 8, 6 and 4, giving $8 + 6 + 4 = \textbf{18}$.

Additional Information

• The trap is answering with the even digits of the original number. Those were 6, 4 and 2, which after transformation are the ones that stayed even — but a candidate who sums the originals gets $6+4+2 = 12$, and one who sums all new digits gets 34.
• Note that adding or subtracting 2 preserves parity: an even digit stays even and an odd digit stays odd. So the even digits of the new number are exactly the transformed versions of the original even digits — a shortcut that skips rewriting the whole number.
• Work left to right and write the new number out before answering. Attempting to track the transformation mentally across seven digits is where errors occur.
• Read the final instruction carefully: the question asks for a sum of selected digits, not the new number itself.