Find the missing term: 16 : 56 :: 32 : ?

Introduction / Context:
This is a number analogy. We infer the rule that maps 16 to 56 and apply the same rule to 32 to obtain the missing term.

Given Data / Assumptions:

• Analogy format: 16 → 56; 32 → ?
• Assume a single consistent transformation across the pair.

Concept / Approach:
Test a constant multiplier first, since 56/16 = 3.5 is a clean ratio and such proportional relations are common in short analogies. If the left mapping is “multiply by 3.5,” the same factor should hold for 32.

Step-by-Step Solution:

Verification / Alternative check:
Alternative nonlinear fits are unnecessary when a constant multiplier explains the first pair exactly.

Why Other Options Are Wrong:
They imply different multipliers (e.g., 3, 4, 4.375, 5) that would not map 16 to 56.

Common Pitfalls:
Overcomplicating the relation with squares/cubes when a simple constant factor works perfectly.

Final Answer:
112