GREAT : 25 :: NUMBER : ? — Identify the rule that maps each word to a number and compute the value for NUMBER.

Introduction / Context:
Word-to-number analogies often encode a simple property of the word such as letter count or a function of it. “GREAT” maps to 25. The most economical hypothesis is 5 letters → 5^2 = 25. We must apply the same rule to “NUMBER.”

Given Data / Assumptions:

• GREAT has 5 letters and maps to 25.
• NUMBER has 6 letters.
• Assume the rule depends on letter count squared.

Concept / Approach:
Test the square-of-length rule: length(GREAT) = 5 → 25; length(NUMBER) = 6 → 36. This rule is consistent, simple, and matches an available option.

Step-by-Step Solution:
1) Count letters of GREAT: 5.2) Compute 5^2 = 25 (matches given).3) Count letters of NUMBER: 6; compute 6^2 = 36.

Verification / Alternative check:
Other encodings (sum of alphabet positions, consonant counts) are possible but needlessly complex and unlikely to yield exactly 25 for GREAT without contrivance. The square-of-length rule is the most parsimonious.

Why Other Options Are Wrong:

• 38, 27, 24: Do not arise from squaring letter count for NUMBER (6).

Common Pitfalls:
Overcomplicating the mapping when a straightforward rule already fits the evidence perfectly.

Final Answer:
36