In this number analogy, “121 is to 12 as 25 is to ______”. Select the number that completes the analogy by following the same square root plus one pattern used in the first pair.

Introduction / Context:
This analogy connects each first number with its second number through a operation built on square roots. The pair 121 : 12 suggests that the second number is not simply the square root but slightly larger. Identifying this pattern and applying it to the second first number, 25, will give the correct related number. Recognising standard squares and using small adjustments like plus or minus one is a common technique in aptitude problems.

Given Data / Assumptions:

• First pair: 121 and 12. • Second pair: 25 and an unknown number. • Options: 5, 6, 7, 8. • Basic square facts: 11² = 121 and 5² = 25.

Concept / Approach:
First, recognise that 121 is a perfect square. Its square root is 11. The second number in the pair is 12, which is exactly one more than 11. This suggests the pattern: second number = square root of first number plus 1. We then apply this same rule to 25. The square root of 25 is 5, and adding 1 gives 6. Among the options, 6 matches this result.

Step-by-Step Solution:
Step 1: Express 121 as a square. 121 = 11 * 11 = 11². Step 2: Relate 11 to 12. 12 = 11 + 1, so the second number is the square root plus one. Step 3: Express 25 as a square. 25 = 5 * 5 = 5². Step 4: Apply the same rule to 25. Square root of 25 is 5. Add one: 5 + 1 = 6. Step 5: Match the result with the options; 6 is option B.

Verification / Alternative check:
Consider alternate rules, such as taking square root minus one. For 121, that would give 10, not 12, so that rule is not valid. Another idea might be to divide the number by 10 or 11, but such operations do not produce a simple pattern that extends to 25 and matches an option. The square root plus one pattern is consistent and uses familiar arithmetic. Additionally, applying this rule to any other perfect square such as 36 would give 6 + 1 = 7, keeping the structure logically stable.

Why Other Options Are Wrong:
• 5: This is exactly the square root of 25 but does not include the extra one seen in the first pair. • 7 and 8: These are larger than the square root plus one and do not follow the established rule.

Common Pitfalls:
A very common mistake is to assume that the second number is always just the square root of the first and select 5 for the second pair. This ignores the important detail of the extra one in 121 : 12. Carefully checking how the square root relates to the second number, whether plus or minus one, is crucial for full accuracy in analogy problems built on squares.

Final Answer:
The number that correctly completes the analogy is 6.