In the following number analogy question, 695 is related to 659 according to a specific pattern formed by rearranging its digits. Using the same rule, 839 will be related to which of the following numbers?

Introduction / Context:
This is a classic number analogy problem where you are given one pair of related numbers (695 : 659) and asked to find a number that relates to 839 in the same way. Such questions check your ability to spot patterns in the arrangement of digits rather than just arithmetic operations like addition, subtraction or multiplication.

Given Data / Assumptions:

• Given analogy: 695 : 659.
• Target: 839 : ?
• Options: 392, 984, 931, 893.
• We assume the pattern involves rearranging or manipulating the digits of the original number.

Concept / Approach:
Instead of directly applying operations such as addition or subtraction to the entire number, it is often useful in analogy questions to look at the digits separately. We check whether the second number is formed by rearranging the digits of the first number in some fixed way. Once we identify the rule for 695 transforming into 659, we apply the same rule to 839 and see which option matches.

Step-by-Step Solution:
Step 1: Write the digits of 695 as 6, 9 and 5. Step 2: Observe the digits of 659: 6, 5 and 9. Step 3: Compare the two sequences. The first digit 6 remains the same in both numbers. The last two digits 9 and 5 in 695 have simply exchanged positions to become 5 and 9 in 659. Step 4: Thus, the rule appears to be: keep the first digit unchanged and swap the second and third digits of the original number. Step 5: Apply this rule to 839. The digits of 839 are 8, 3 and 9. Keeping the first digit 8 fixed and swapping the last two digits 3 and 9 gives 8, 9, 3. Step 6: The resulting number is 893. Check the options: 893 matches option D.

Verification / Alternative check:
To ensure the rule is consistent, verify that no other obvious pattern exists that would point to a different option. There is no simple arithmetic relation such as 695 minus a fixed value to get another option and then repeating the same for 839. Additionally, none of the other options 392, 984 or 931 arise from a simple swap of the last two digits of 839. This confirms that our digit rearrangement rule is both simple and unique.

Why Other Options Are Wrong:
392 is formed by a different digit arrangement and does not keep the first digit of 839 fixed. 984 changes both the first digit and the order of the remaining digits, which does not follow the pattern from 695 to 659. 931 again does not keep the first digit unchanged and does not result from just swapping the last two digits of 839. Only 893 is obtained by preserving the first digit and interchanging the last two digits, which matches the original example.

Common Pitfalls:
Students sometimes jump to arithmetic operations such as subtracting or adding a fixed number, which can mislead them when the pattern is purely positional. Another common error is to overcomplicate the rule by combining digit sums and products when a simple swap is sufficient. Always start by checking the simplest possible pattern: digit rearrangement, reversal, or swapping.

Final Answer:
Using the same digit-swapping rule, the number related to 839 is 893.