Select the related number from the options: 456 : 15 :: 789 : ? in this number analogy.

Introduction / Context:
This problem is a simple number analogy that tests your ability to find patterns involving digits. The pair 456 and 15 is given, and you have to identify how those two numbers are related and then apply the same logic to 789. Such questions are common in aptitude tests because they check observation and basic arithmetic skills.

Given Data / Assumptions:
1) The first number in the model pair is 456.
2) The second number in that pair is 15.
3) The new first number is 789, and we must find its corresponding second number.
4) The options given are 22, 24, 26, and 28.
5) The relationship is likely based on simple operations with the digits such as addition or multiplication.

Concept / Approach:
A standard first check in such questions is to examine the sum of digits or the product of digits. When you calculate the sum of digits of 456, you obtain 4 plus 5 plus 6. If this matches 15, then the pattern is clear. After confirming this, applying the same operation to the second number 789 will lead directly to the answer. This approach is simple, systematic, and avoids guesswork.

Step-by-Step Solution:
Step 1: Break 456 into its digits: 4, 5, and 6. Step 2: Add these digits. 4 + 5 + 6 equals 15. This matches the second number in the model pair. Step 3: Conclude that the rule is to sum the digits of the three digit number in order to obtain the related number. Step 4: Now apply the same rule to the number 789. Break it into digits 7, 8, and 9. Step 5: Add the digits. 7 + 8 + 9 equals 24. Step 6: Look at the answer options and identify 24 as one of them. Step 7: Therefore, 789 is related to 24 in the same way that 456 is related to 15.

Verification / Alternative check:
Check that no other option can be produced by a simpler or more natural operation consistent with the first pair. For example, multiplying the digits of 456 gives 4 * 5 * 6 equals 120, not 15. Subtracting digits does not give 15 either. The sum of digits is the only straightforward operation that perfectly explains 456 to 15 and leads to a unique result for 789.

Why Other Options Are Wrong:
The remaining options 22, 26, and 28 do not equal 7 + 8 + 9 and cannot be obtained by summing the digits of 789. If you chose any of those without a clear pattern, it would be a guess rather than a logical deduction from the given pair. Since competitive exams reward correct pattern recognition, only 24 is acceptable.

Common Pitfalls:
Some candidates may search for an overly complex relationship such as multiplying digits or combining squares, which is unnecessary for this problem. Others may perform the addition incorrectly under time pressure. A disciplined approach is to check simple digit sums first and to compute them carefully.

Final Answer:
Following the same pattern, 789 corresponds to 24, just as 456 corresponds to 15.