Select the related number from the given alternatives: if 30 is related to 16 in a certain way, then 24 is related to which number?

Introduction / Context:
This is a numerical analogy question where the pair 30 : 16 is given, and you must determine the number that should be paired with 24 in the same way. The task is to identify a simple, consistent arithmetic rule that converts 30 into 16 and then apply that rule to 24. Such questions test your ability to spot patterns in numbers quickly and accurately.

Given Data / Assumptions:

• The first pair is 30 on the left and 16 on the right.
• The second pair starts with 24 and we must find the missing number.
• The options for the missing number are 14, 13, 20, and 25.
• We assume that the same arithmetic operation or combination of operations is applied to both 30 and 24.
• The pattern is expected to be simple enough for an aptitude test, such as division, addition, or a combination.

Concept / Approach:
A good first step is to check basic operations: half, double, add or subtract a constant. If we divide 30 by 2, we get 15, which is very close to 16. Adding 1 to this gives exactly 16. So a candidate rule is: take half of the given number and then add 1. We can test this rule on 30 and then apply it to 24. If the computed value matches one of the options, and no simpler competing rule explains the pair, we accept it as the pattern.

Step-by-Step Solution:
Step 1: Consider the first pair. Start with 30. Step 2: Divide 30 by 2. This gives 30 / 2 = 15. Step 3: Add 1 to this result. So 15 + 1 = 16, which matches the given right side of the pair. Step 4: Conclude that the working rule is: result = (given number / 2) + 1. Step 5: Now apply the same rule to 24. First compute 24 / 2 = 12. Step 6: Add 1 to this quotient. So 12 + 1 = 13. Step 7: Check the options and find that 13 is present as option b, so that is the correct answer.

Verification / Alternative check:
We can test for alternative rules, for example subtracting a constant or squaring and then adjusting, but none of those simple attempts give exactly 16 from 30 in a natural way. For instance, 30 minus 14 equals 16, but then 24 minus 14 equals 10, which is not one of the options. The rule (n / 2) + 1 is both simple and consistent, making it the most plausible pattern. Applying it to any other candidate number would not match the given pair, confirming that 13 is the only value that fits the analogy properly.

Why Other Options Are Wrong:
If we take 14, then doubling and subtracting or any similar simple operations do not lead us back to 30 in the first pair. The same is true for 20 and 25. None of these values can be produced by applying the rule (number / 2) + 1 to 24. Selecting any of them would break the consistency between the first and second pairs, which is not allowed in a well formed analogy question.

Common Pitfalls:
A common mistake is to try random operations like adding digits, squaring, or taking differences without first checking the simplest possibilities. Another pitfall is to assume multiplication or division by an arbitrary fraction that does not look natural. In exam situations, always try small integer operations such as half plus or minus one, or double plus or minus one, before moving to complex patterns. This strategy often quickly reveals the intended rule, as in this question.

Final Answer:
Using the rule result = (number / 2) + 1, 30 maps to 16 and 24 maps to 13, so the correct answer is 13.