100 : 121 :: 144 : ? — Recognize the pattern (think squares and successive integers) and compute the missing value.
Verbal Reasoning
Analogy
Difficulty: Easy
Choose an option
Answer
Correct Answer: 169
Explanation
Introduction / Context:Classic numerical analogies often use perfect squares in succession. 100 and 121 are familiar squares (10^2 and 11^2). We leverage that structure to extend the pattern.
Given Data / Assumptions:
- 100 = 10^2; 121 = 11^2.
- 144 = 12^2.
- We expect the mapping to follow 'n^2 → (n+1)^2'.
Concept / Approach:Interpret each term as a perfect square of consecutive integers: 10^2 maps to 11^2; therefore, 12^2 should map to 13^2.
Step-by-Step Solution:1) 100 = 10^2 → 121 = 11^2 confirms +1 on the base.2) 144 = 12^2 → next is 13^2.3) 13^2 = 169.
Verification / Alternative check:Check other options: none are perfect squares of 13 except 169.
Why Other Options Are Wrong:
- 160/93/426/131: Not equal to 13^2; they break the consecutive square pattern.
Common Pitfalls:Mistaking 12^2 as 142 or forgetting that 13^2 is 169.
Final Answer:169