The digits in the number 25673948 are arranged in ascending order from left to right. In this new arrangement, what is the sum of the digit that is fourth from the right and the digit that is third from the left?

Introduction / Context:
This problem combines basic ordering of digits and positional reasoning within a number. We are asked to rearrange the digits of a given number in ascending order and then identify two particular digits according to their positions from the left and from the right. Finally, we must compute the sum of these two digits. It tests careful manipulation of digit sequences and position counting.

Given Data / Assumptions:

• Original number: 25673948.
• Digits must be rearranged in ascending order from left to right.
• In the new arrangement, we must find:
  • The digit that is third from the left.
  • The digit that is fourth from the right.
• The required answer is the sum of these two digits.

Concept / Approach:
First, list all digits of the original number without changing them, then sort them in ascending order. After obtaining the sorted sequence, position counting can be done easily: from the left, positions are counted 1, 2, 3 and so on; from the right, positions are counted starting from the units place. Once the correct digits are identified, adding them gives the final result.

Step-by-Step Solution:
Step 1: Write down the digits of 25673948: 2, 5, 6, 7, 3, 9, 4, 8. Step 2: Arrange these digits in ascending order: 2, 3, 4, 5, 6, 7, 8, 9. Step 3: In the new arrangement, the digit third from the left is the third element in this list. Step 4: The list from the left is: position 1 = 2, position 2 = 3, position 3 = 4, position 4 = 5, position 5 = 6, position 6 = 7, position 7 = 8, position 8 = 9. So the digit third from the left is 4. Step 5: Now count from the right. The rightmost digit (units place) is 9, second from the right is 8, third from the right is 7, and fourth from the right is 6. Step 6: Therefore, the digit fourth from the right is 6. Step 7: The required sum is 4 + 6 = 10.

Verification / Alternative check:
We can also mark positions explicitly under the ascending sequence 2 3 4 5 6 7 8 9. Label positions from the left as 1 through 8 and from the right as 1 through 8 in reverse order. This clearly shows that the third from the left is 4 and the fourth from the right is 6. Adding them again confirms the total of 10.

Why Other Options Are Wrong:
Sums of 9, 8 or 6 arise only if one of the positional digits is misidentified, for example by confusing the third from the left with the fourth, or miscounting from the right.

Common Pitfalls:
Errors often occur when students miscount positions from the right, especially in an 8 digit sequence, or forget to fully reorder the digits before counting. Another pitfall is to overlook repeated digits (though in this number all digits are distinct). Sorting the digits first and then carefully counting positions from both ends helps avoid these issues.

Final Answer:
The required sum is 10.