If 2 is added to each odd digit and 3 is subtracted from each even digit in the number 7843651, how many digits will appear more than once in the new number thus formed?

The correct option is Two.

Let us solve this step-by-step by applying the given conditions to the original number.

Original Number: 7843651

Rules given:
1. If a digit is odd, add 2 to it.
2. If a digit is even, subtract 3 from it.

Now, let us process each digit of the number 7843651 from left to right:

• First digit: 7 (odd)
$7+2=9$

• Second digit: 8 (even)
$8-3=5$

• Third digit: 4 (even)
$4-3=1$

• Fourth digit: 3 (odd)
$3+2=5$

• Fifth digit: 6 (even)
$6-3=3$

• Sixth digit: 5 (odd)
$5+2=7$

• Seventh digit: 1 (odd)
$1+2=3$

New Number Formed: 9515373

Let us check the frequency of each digit appearing in the new number 9515373:

• 9 appears 1 time.
• 5 appears 2 times (more than once).
• 1 appears 1 time.
• 3 appears 2 times (more than once).
• 7 appears 1 time.

The digits that appear more than once are 5 and 3.

Therefore, exactly 2 digits appear more than once in the new number.