The digits of the number 79246358 are arranged in descending order from left to right to form a new eight digit number. In this new arrangement, what is the difference between the digit in the third position from the right and the digit in the second position from the left?

Introduction / Context:
Questions involving rearrangement of digits test attention to detail, place value understanding, and the ability to follow multi step instructions. In this problem, we are asked to rearrange digits of an eight digit number in descending order and then identify digits at specific positions from left and right, followed by a subtraction. Such questions are common in arithmetic reasoning sections and require careful, organized work to avoid simple mistakes.

Given Data / Assumptions:

• Original number: 79246358.
• Digits must be arranged in descending order from left to right.
• We then consider the new eight digit number formed after rearrangement.
• We need the digit in the second position from the left.
• We also need the digit in the third position from the right.
• The required answer is the difference between these two digits.

Concept / Approach:
First, we list all digits of the number and sort them in descending order. Once we form the new number, we locate the digit at the required positions. Position counting from the left starts at the leftmost digit as first. Position counting from the right starts at the rightmost digit as first. After identifying both digits, we compute their difference, usually as the larger digit minus the smaller digit, in order to get a non negative result.

Step-by-Step Solution:
Step 1: Write down all digits of 79246358: they are 7, 9, 2, 4, 6, 3, 5, and 8. Step 2: Arrange these digits in descending order: 9, 8, 7, 6, 5, 4, 3, 2. Step 3: The new number formed is 98765432. Step 4: Identify the digit in the second position from the left: the digits from left are 9 (first), 8 (second), so the required left side digit is 8. Step 5: Identify the digit in the third position from the right: from right we have 2 (first), 3 (second), 4 (third), so the required right side digit is 4. Step 6: Find the difference between these digits: 8 minus 4 = 4.

Verification / Alternative check:
To verify, we can double check the ordering and positions. The descending sequence of digits from 9 to 2 is standard and easy to recall. Recounting from the left gives 9, 8, 7, 6, 5, 4, 3, 2, so the second digit is clearly 8. Counting from the right gives 2, 3, 4, 5, 6, 7, 8, 9, so the third digit from the right is 4. Performing the subtraction again confirms the difference is 4. As an additional check, we can quickly review that no digits were omitted or duplicated incorrectly in the rearranged number.

Why Other Options Are Wrong:
1: This would require the two digits to differ by only one step, which does not match 8 and 4.
2: This also does not match 8 minus 4 and suggests a mis count of positions.
3: This would match 7 and 4 or 8 and 5, so it indicates errors in digit selection.
5: This would require a combination like 9 and 4, so it again reflects incorrect placement or arithmetic.

Common Pitfalls:
A major source of error is confusing the direction of position counting, especially third from the right versus third from the left. Another frequent mistake is mis ordering digits when arranging them in descending sequence, for example slipping into 98764532. Under exam pressure, candidates might also rush the subtraction step. To avoid these, it is helpful to write the rearranged number clearly, mark positions, and perform the final subtraction carefully.

Final Answer:
After rearranging and checking the required positions, the difference between the two digits is 4.