Number Analogy — “20 : 50 :: 100 : ?”. Identify the same multiplication pattern that maps 20 to 50 and apply it to 100.

Introduction / Context:
In numeric analogies, the goal is to uncover the exact arithmetic rule that transforms the first number into the second, and then replicate that rule on the third number to obtain the fourth. Here, 20 becomes 50; we must determine the factor or operation responsible and apply it to 100.

Given Data / Assumptions:

• 20 maps to 50 via a consistent arithmetic operation.
• We seek a single-step rule that also yields an integer when applied to 100.
• All options are plausible integers; only one matches the discovered rule.

Concept / Approach:
Compute the ratio 50 / 20 = 2.5. Thus, the mapping can be modeled as “multiply by 2.5”. If this rule is correct, then 100 should map to 100 * 2.5 = 250. This is the cleanest, single-operation explanation consistent with the pair.

Step-by-Step Solution:

Verification / Alternative check:
Try addition: 20 + 30 = 50, but then 100 + 30 = 130 (not an option). Try proportional addition like “add 150% of 20,” which is equivalent to *2.5. The multiplication rule is more general and replicable.

Why Other Options Are Wrong:

Common Pitfalls:
Assuming addition/subtraction when a proportional (multiplicative) rule fits exactly. Always test the simplest exact ratio first.

Final Answer:
250