In the following question, select the related number pair from the given alternatives: 11 is to 16 as which of the following pairs?

Introduction / Context:
This question presents a simple number pair analogy. The pair 11 : 16 is given, and you must select from the options the pair that is related in the same way. In many such questions, the relationship between the numbers in the pair is a fixed difference, and the correct answer is another pair that shares that same difference.

Given Data / Assumptions:

• The base pair is 11 on the left and 16 on the right.
• The candidate pairs are 14 : 16, 15 : 22, 7 : 14, and 13 : 18.
• We assume that the relationship is likely to be a simple arithmetic one such as adding a constant to the first number.
• The task is to find which pair exhibits the same numerical difference as 11 and 16.

Concept / Approach:
We start by computing the difference between the numbers in the base pair. 16 minus 11 equals 5. This suggests a rule of adding 5 to obtain the second number from the first. We then check each candidate pair and see which one also satisfies a difference of 5 between its elements. The pair that matches this difference is the correct answer, as it preserves the structure of the original relationship.

Step-by-Step Solution:
Step 1: Compute the difference in the base pair. 16 - 11 = 5, so the second number is 5 greater than the first. Step 2: Examine option a, 14 : 16. The difference here is 16 - 14 = 2, which does not equal 5. Step 3: Examine option b, 15 : 22. The difference is 22 - 15 = 7, not 5. Step 4: Examine option c, 7 : 14. The difference is 14 - 7 = 7, again not 5. Step 5: Examine option d, 13 : 18. The difference is 18 - 13 = 5. Step 6: Conclude that in the pair 13 : 18, the same rule second = first + 5 is satisfied.

Verification / Alternative check:
Because the question does not offer additional context, the simplest explanation is usually preferred. The pattern of adding 5 is straightforward and consistent: 11 + 5 = 16 and 13 + 5 = 18. If we tried more complex operations, such as multiplication or squaring, we would not find a natural rule that matches both the original pair and any option. Hence, the constant difference pattern is the most reasonable and confirms that 13 : 18 is correct.

Why Other Options Are Wrong:
The pair 14 : 16 shows a difference of 2, not 5. The pairs 15 : 22 and 7 : 14 each show a difference of 7, which again does not match the original difference. Using any of these would introduce inconsistency in the analogy, because the basic rule linking the numbers in each pair would be different from that of 11 : 16.

Common Pitfalls:
Candidates sometimes search for hidden patterns like prime relationships or digit manipulations when a simple constant difference is sufficient. Another common mistake is not performing the subtraction carefully, which can lead to misidentifying the matching pair. A quick scan of differences, done accurately, is usually enough to solve such problems efficiently.

Final Answer:
Since 16 is 5 more than 11, the pair that mirrors this relationship is 13 : 18, where 18 is also 5 more than 13.