In this digit based number analogy, “9143 is to 9963 as 6731 is to ______”. Select the number that completes the analogy by following the same digit sum transformation pattern used in the first pair.

Introduction / Context:
This question involves a number analogy where the transformation is based on the sum of the digits rather than a direct multiplication or addition on the whole number. The pair “9143 : 9963” does not appear to follow a simple increase such as adding a fixed constant to 9143. Instead, if we look at the sum of the digits, a clear and consistent rule emerges. We must apply that same rule to 6731 to find the correct partner from the options.

Given Data / Assumptions:

• First pair: 9143 corresponds to 9963. • Second pair: 6731 corresponds to ? • Options: 1368, 5666, 8964, 9694. • We focus on the sum of digits as a possible key transformation because the raw differences between the numbers are not simple multiples.

Concept / Approach:
Compute the sum of the digits of 9143 and 9963. For 9143, the sum is 9 + 1 + 4 + 3. For 9963, the sum is 9 + 9 + 6 + 3. This transformation increases the digit sum by a constant amount. Then, we look at 6731, compute its digit sum, and search for the answer choice whose digit sum is larger by the same constant amount as in the first pair. This gives us a consistent rule that works across both examples.

Step-by-Step Solution:
Step 1: Compute the sum of the digits of 9143. 9 + 1 + 4 + 3 = 17. Step 2: Compute the sum of the digits of 9963. 9 + 9 + 6 + 3 = 27. Step 3: Observe the pattern. The digit sum increases from 17 to 27, which is an increase of 10. Step 4: Compute the sum of the digits of 6731. 6 + 7 + 3 + 1 = 17. Step 5: Apply the same rule. We need a related number whose digit sum is 17 + 10 = 27. Step 6: Check each option. 1368: 1 + 3 + 6 + 8 = 18 (not 27). 5666: 5 + 6 + 6 + 6 = 23 (not 27). 8964: 8 + 9 + 6 + 4 = 27 (matches 27). 9694: 9 + 6 + 9 + 4 = 28 (not 27). Only 8964 has the required digit sum of 27.

Verification / Alternative check:
The structure of the rule is simple and consistent: for each input four digit number, form a new four digit number whose digit sum is exactly 10 more than the original. For 9143, 17 becomes 27 in 9963. For 6731, 17 must again become 27. Among the options, only 8964 satisfies this requirement. While many different four digit numbers have a digit sum of 27, the exam question restricts us to the given choices, and within that set, the rule identifies a single unique answer.

Why Other Options Are Wrong:
• 1368: Digit sum is 18, so the increase is from 17 to 18, not from 17 to 27. • 5666: Digit sum is 23, again not 27. • 9694: Digit sum is 28, which is 11 more than 17 rather than 10 more.

Common Pitfalls:
Some test takers may search for a direct additive or multiplicative relationship between 9143 and 9963 and become stuck, because the numbers are not simple multiples. Others may look for patterns in individual digits without considering the digit sum. When raw arithmetic fails, it is often helpful to check the behaviour of digit sums, which frequently appears in reasoning questions and gives a clean and testable rule here.

Final Answer:
The number that correctly completes the analogy is 8964.