63 : 21 :: 27 : ? — Determine the operation applied to the first number to obtain the second, then apply it to find the missing term.

Introduction / Context:
Simple arithmetic analogies often involve a fixed operation. Here, 63 maps to 21, which naturally suggests division by 3. Apply the same operation to 27 to find the missing term.

Given Data / Assumptions:

• 63 → 21.
• We must find 27 → ? using the same rule.

Concept / Approach:
If 63/3 = 21, then the operation is “divide by 3.” Apply it consistently: 27/3 = 9. This is the most straightforward, consistent mapping.

Step-by-Step Solution:
1) Test division by 3 on 63: 63/3 = 21 (fits).2) Apply to 27: 27/3 = 9.3) Choose 9.

Verification / Alternative check:
Check alternatives (subtract 42; divide by 3 is far more natural and symmetric for both numbers).

Why Other Options Are Wrong:

• 6, 3, 1: Do not result from the same simple rule applied to both pairs.

Common Pitfalls:
Trying more complex operations when a single consistent division explains both pairs cleanly.

Final Answer:
9