How many such digits are there in the number 7346285 which are at the same position from the beginning of the number as they would be when the digits are arranged in ascending order?

Introduction / Context:
This question asks you to compare the positions of digits in a given number with their positions when the digits are sorted in ascending order. You must count how many digits remain in the same position under both arrangements. This tests your understanding of order and careful comparison of positions.

Given Data / Assumptions:

- The original number is 7346285.- We rearrange its digits in ascending order to compare positions.- We assume all digits are considered independently and positions are counted from the left starting at 1.

Concept / Approach:
First, list the digits of the number with their original positions. Then sort the digits in ascending order and list them again with new positions. A digit counts as qualifying if the digit at a particular position in the original number is the same as the digit at the same position in the sorted list. Since all digits here are distinct, we simply match by value and position directly.

Step-by-Step Solution:
Step 1: Write the original digits with positions: 7(1), 3(2), 4(3), 6(4), 2(5), 8(6), 5(7).Step 2: Arrange these digits in ascending order: 2, 3, 4, 5, 6, 7, 8.Step 3: In the ascending list, positions are: 2(1), 3(2), 4(3), 5(4), 6(5), 7(6), 8(7).Step 4: Compare position by position. At position 1, original has 7, ascending has 2, so no match.Step 5: At position 2, original has 3 and ascending has 3, so this is a match.Step 6: At position 3, original has 4 and ascending has 4, so this is another match.Step 7: At positions 4, 5, 6 and 7, the digits do not match the ascending list. Therefore, only positions 2 and 3 qualify.

Verification / Alternative check:
List the two matching positions explicitly: position 2 with digit 3, and position 3 with digit 4. Since no other positions have the same digit in both the original and the ascending arrangement, the total number of such digits is exactly two. A second scan confirms that no other accidental matches are being missed.

Why Other Options Are Wrong:
Option None is incorrect because we have found two valid matches. Option one undercounts the correct answer, and option Three overestimates, as there is no third position where the digit remains unchanged after sorting. Thus, only option Two accurately reflects the count.

Common Pitfalls:
Errors usually occur when candidates confuse the notion of digit value with position or when they fail to list all positions carefully. Some may also misinterpret the question as counting identical digits in both arrangements without regard to position. The key is to focus specifically on digits that occupy the same position number in both versions of the number.

Final Answer:
The number of such digits is two.