100 : 121 :: 144 : ? — Recognize the square-number sequence and supply the next mapped value.

Introduction / Context:
This analogy uses consecutive squares. 100 = 10^2 maps to 121 = 11^2. Therefore 144 = 12^2 should map to 169 = 13^2. The task is to identify the consistent square progression across both pairs.

Given Data / Assumptions:

• 10^2 → 11^2.
• 12^2 → ?
• We maintain the “next integer squared” rule.

Concept / Approach:
Apply the same increment to the base before squaring: from 10 to 11; from 12 to 13. Thus, 144 should map to 169.

Step-by-Step Solution:
1) Recognize 100 and 121 as consecutive squares (10^2, 11^2).2) Recognize 144 as 12^2.3) Map to 13^2 = 169.

Verification / Alternative check:
Confirm 169 = 13*13. The pattern holds uniformly.

Why Other Options Are Wrong:

• 160, 93, 426: Not perfect squares and do not fit the defined pattern.

Common Pitfalls:
Missing that both pairs are squares and instead trying ad hoc arithmetic differences.

Final Answer:
169