In this number analogy, “15 is to 225 as 12 is to ______”. Select the number that completes the analogy by applying the same squaring pattern used in the first pair.

Introduction / Context:
This question uses a straightforward square based pattern. The pair 15 : 225 shows that the second number is the square of the first number. The task is to apply the same pattern to 12 and select the correct result from the options. Recognising when a number is the square of another is an essential skill in quantitative aptitude, especially in analogy and series questions.

Given Data / Assumptions:

• First pair: 15 and 225. • Second pair: 12 and an unknown number. • Options: 144, 122, 112, 222. • Basic fact: 15² = 225.

Concept / Approach:
Check whether the second number in the first pair is the square of the first. Since 15 * 15 = 225, the pattern is clear: second number = first number squared. We then apply the same operation to the second first number, 12. So the required second number should be 12². After computing 12², we match the result with the options and choose the one that fits exactly.

Step-by-Step Solution:
Step 1: Confirm the relationship in the first pair. Compute 15²: 15 * 15 = 225. So the second number is the square of the first. Step 2: Apply the same rule to 12. Compute 12²: 12 * 12 = 144. Step 3: Compare 144 with the options. Option A is 144, which matches the computed square exactly.

Verification / Alternative check:
We can rule out other types of operations quickly. For example, multiplying 15 by 10 gives 150, not 225. Adding a constant would not match 225 exactly either. Because 225 is a familiar square, identifying it as 15² is straightforward. Similarly, 144 is a well known square of 12. This symmetry strongly supports the square pattern as the intended logic for this analogy.

Why Other Options Are Wrong:
• 122 and 112: These are not perfect squares of integer values close to 12 and have no clear link to 12 in a simple square based rule. • 222: Only superficially resembles 225 in digits, but does not represent the square of 12 or any similar pattern.

Common Pitfalls:
Occasionally students misread 225 and assume some addition based pattern, for example adding 210 to 15. Such a rule is not meaningful and does not generalise to 12. To avoid this, always test whether a number is a perfect square when numbers like 225 and 144 appear. Recognising these squares saves time and improves accuracy on many evaluation questions.

Final Answer:
The number that correctly completes the analogy is 144.