3 : 27 :: 4 : ? — Determine the operation connecting 3 to 27 and apply it to 4 to find the missing number.

Introduction / Context:
The pair 3 : 27 suggests exponentiation, as 27 is 3^3. Similar cube patterns are common in analogy questions and extend naturally to the next input.

Given Data / Assumptions:

• 27 = 3^3.
• We assume the same transformation is applied to 4.

Concept / Approach:
If the rule is 'n → n^3', then 4 must map to 4^3.

Step-by-Step Solution:
1) Confirm 3 → 3^3 = 27.2) Apply to 4: 4^3 = 64.

Verification / Alternative check:
Scan options; 64 is present and matches 4^3.

Why Other Options Are Wrong:

• 16/32/28/81: These represent 4^2, 2^5, 4*7, and 3^4 respectively; none equals 4^3.

Common Pitfalls:
Confusing square and cube operations or miscomputing 4^3.

Final Answer:
64