Multiplicative pattern analogy If 3 maps to 12, determine the analogous value when 5 maps to ?

Introduction / Context:
This is a basic numeric analogy using a simple polynomial-like pattern: multiply a number by its successor. Such questions check fluency with quick mental arithmetic and pattern transfer.

Given Data / Assumptions:

• 3 maps to 12.
• The mapping must be consistent for 5.

Concept / Approach:
Notice that 12 = 3 * 4 = n * (n + 1). This is a common pattern in reasoning sets.

Step-by-Step Solution:
Identify rule: f(n) = n * (n + 1).Apply to n = 5 → 5 * 6 = 30.

Verification / Alternative check:
Check for 3: 3 * 4 = 12 matches the given pair. Hence, the rule is validated.

Why Other Options Are Wrong:
25: Equals 5^2, not n(n + 1).35: Equals 5 * 7, skipping the immediate successor.15: Equals 3 * 5, an unrelated product.

Common Pitfalls:
Squaring the number or multiplying by the next odd/even rather than the immediate successor.

Final Answer:
30