For the numbers 567, 284, 696, 865 and 738, one is added to the last digit of each number and then the order of the digits is reversed. Which original number will become the fourth smallest number after this transformation?

Introduction / Context:
This question blends digit manipulation with ordering of numbers. Each original three digit number undergoes a specific two step transformation: first the unit digit is increased by one, and then the entire three digit sequence is reversed. After performing this transformation on each number, you must determine which original number corresponds to the fourth smallest transformed value.

Given Data / Assumptions:
- Original numbers: 567, 284, 696, 865, 738. - Step 1: Add one to the last digit of each number. - Step 2: Reverse the order of the three digits of the resulting number. - None of the given numbers ends in 9, so we do not need to handle carrying over to a new digit.

Concept / Approach:
The approach is to apply the given two step operation carefully to each number. Then, list all transformed numbers and sort them in ascending order. Once the sorted order is clear, you can identify which transformed number is the fourth smallest and map it back to its original number. The critical part is consistent application of the same transformation rule to every number without arithmetic slips.

Step-by-Step Solution:
Step 1: Transform 567. Adding one to the last digit 7 gives 568. Reversing 568 yields 865. Step 2: Transform 284. Last digit 4 plus one gives 5, so we get 285. Reversing 285 yields 582. Step 3: Transform 696. Last digit 6 plus one gives 7, therefore the intermediate number is 697. Reversing 697 yields 796. Step 4: Transform 865. Last digit 5 plus one gives 6, so we get 866. Reversing 866 yields 668. Step 5: Transform 738. Last digit 8 plus one gives 9, so we get 739. Reversing 739 yields 937. Step 6: Collect the transformed numbers: 865 (from 567), 582 (from 284), 796 (from 696), 668 (from 865), 937 (from 738). Step 7: Arrange these values in ascending order: 582, 668, 796, 865, 937. Step 8: The fourth smallest among these is 865, which came from the original number 567.

Verification / Alternative check:
Given the small number of values, you can easily double check by rewriting a table that shows each original number next to its transformed version. Make sure that each reversal is correct: for example, reversing 568 should indeed give 865, not 856. After verifying each transformation, sort again mentally or on paper. The order 582, 668, 796, 865, 937 is straightforward and clearly places 865 fourth. This confirms that 567 is the correct original number.

Why Other Options Are Wrong:
284: Its transformed value 582 is the smallest number, not the fourth smallest. 865: Its transformed value 668 is the second smallest, not the fourth smallest. 738: Its transformed value 937 is the largest, not the fourth smallest.

Common Pitfalls:
Some students reverse the digits first and then add one to the last digit, which reverses the intended order of operations and produces incorrect results. Others may misorder the transformed numbers because they mentally compare only the first digit instead of the full three digit values. Writing down each intermediate step and carefully sorting helps avoid these errors, especially under time constraints.

Final Answer:
The original number that becomes the fourth smallest after the described transformation is 567.