In the number 94257636, if 2 is subtracted from each odd digit and 3 is added to each even digit, a new number is formed. In this new number, how many distinct digits appear exactly twice?

Introduction / Context:
This arithmetic reasoning question tests your ability to work carefully with digits and simple transformation rules. Starting from an eight digit number, you are asked to apply different operations to odd and even digits and then count how many distinct digits appear exactly twice in the transformed number. It is a good exercise in attention to detail and counting.

Given Data / Assumptions:

• The original number is 94257636.
• For each odd digit, subtract 2 to get the new digit.
• For each even digit, add 3 to get the new digit.
• The digits are transformed independently, position by position.
• We must examine the resulting sequence of digits and count how many different digit values occur exactly twice.

Concept / Approach:
The method is straightforward: process the number digit by digit. Identify whether each digit is odd or even, apply the required arithmetic, and write down the new digit. After obtaining the new eight digit sequence, count how many times each distinct digit appears. The question is not asking how many times digits repeat in total, but how many distinct digit values have a frequency of exactly two in the new number.

Step-by-Step Solution:
Step 1: Write the digits of 94257636: 9, 4, 2, 5, 7, 6, 3, 6. Step 2: Apply the rule: odd digits → subtract 2; even digits → add 3. Step 3: 9 (odd) becomes 9 - 2 = 7. Step 4: 4 (even) becomes 4 + 3 = 7. Step 5: 2 (even) becomes 2 + 3 = 5. Step 6: 5 (odd) becomes 5 - 2 = 3. Step 7: 7 (odd) becomes 7 - 2 = 5. Step 8: 6 (even) becomes 6 + 3 = 9. Step 9: 3 (odd) becomes 3 - 2 = 1. Step 10: 6 (even) becomes 6 + 3 = 9. Step 11: The new sequence is 7, 7, 5, 3, 5, 9, 1, 9.

Verification / Alternative check:
Count the frequency of each digit in the new number. Digit 7 appears twice, digit 5 appears twice, digit 9 appears twice, digit 3 appears once, and digit 1 appears once. Therefore, three distinct digits (7, 5, and 9) each occur exactly twice. The correct count is therefore 3.

Why Other Options Are Wrong:
Option A 0 would mean no digit appears exactly twice, which is not true. Option B 1 and option C 2 both underestimate the actual number of distinct digits that appear two times. They could result from miscalculating one or two of the transformations or miscounting frequencies.

Common Pitfalls:
A typical mistake is to misclassify a digit as odd or even, especially 0, 2, 4, 6, and 8, or to perform subtraction and addition incorrectly when doing the transformations mentally. Another error occurs when counting frequencies quickly without writing them down. Listing the new digits clearly and tallying each distinct value prevents these errors.

Final Answer:
In the new number, 3 distinct digits appear exactly twice.