Each of the following three digit numbers has its first and third digits interchanged: 987, 514, 658, 487, 404 and 269. After this interchange, which digit will be the third digit (units place) of the second lowest number obtained?

Introduction / Context:
This problem involves manipulating three digit numbers by swapping their first and third digits and then comparing the resulting numbers. It tests the understanding of place value in decimal numbers and the ability to order a list of numbers correctly after a specified transformation. Finally, it asks for a particular digit in the second smallest transformed number.

Given Data / Assumptions:

• Original numbers: 987, 514, 658, 487, 404, 269.
• For each number, the first and third digits are interchanged.
• We then form a new list of six transformed numbers.
• We must arrange these new numbers in ascending order and find the units digit (third digit) of the second lowest number in this new arrangement.

Concept / Approach:
Three digit numbers can be written as ABC, where A is the hundreds digit, B is the tens digit and C is the units digit. Swapping the first and third digits converts ABC into CBA. For each given original number, we apply this rule to get the new number. After calculating all transformed numbers, we compare them to determine their order from smallest to largest. Finally, we pick the second smallest transformed number and note its third digit, which is simply its units digit.

Step-by-Step Solution:
Step 1: Transform each number by swapping its first and third digits. 987 becomes 789. 514 becomes 415. 658 becomes 856. 487 becomes 784. 404 remains 404 because the first and third digits are both 4. 269 becomes 962. Step 2: List all transformed numbers: 789, 415, 856, 784, 404, 962. Step 3: Arrange these numbers in ascending order: 404, 415, 784, 789, 856, 962. Step 4: The second lowest number in this ordered list is 415. Step 5: The third digit (units place) of 415 is 5.

Verification / Alternative check:
One can quickly recheck by confirming that 404 is indeed the smallest, since its hundreds digit is 4 and all others begin with 7, 8 or 9. Among the remaining numbers, 415 has hundreds digit 4 and tens digit 1, making it larger than 404 but smaller than any number starting with 7 or 8. Therefore it must be the second lowest, and its units digit is clearly 5, confirming the result.

Why Other Options Are Wrong:
Digit 4 corresponds to the units of 404 or another number, but not to the second smallest transformed number. Digits 8 and 9 appear in larger transformed numbers like 784, 789, 856 or 962 and cannot be the units digit of the second lowest number 415.

Common Pitfalls:
Some students mistakenly interchange the middle digit instead of the first and third digits, or treat the numbers as if only one swap were required among the list. Others forget to re order all the transformed numbers and instead try to read off digits directly from the initial list. Carefully transforming each number and then fully sorting them avoids these errors.

Final Answer:
The third digit of the second lowest transformed number is 5.