Identify the odd number: Three are squares of prime numbers (13^2, 17^2, 19^2 after repair), while one is a square of a composite number (15^2). Choose the square of the composite.
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A169
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B225
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C289
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D361
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ENone of these
Answer
Correct Answer: 225
Explanation
Introduction / Context:The original options contained a duplicate “225”. Under the Recovery-First policy, we minimally repair by treating the fourth entry as the next consistent prime square, 361 (which is 19^2). Now the set contrasts prime squares with one composite-base square.
Given Data / Assumptions:
- 169 = 13^2 (prime base).
- 289 = 17^2 (prime base).
- 361 = 19^2 (prime base).
- 225 = 15^2 (composite base; 15 = 3 * 5).
Concept / Approach:Classify by the nature of the base n whose square forms n^2: prime vs composite.
Step-by-Step Solution:
Check bases: 13, 17, 19 are prime; 15 is composite.Therefore 225 (15^2) is distinct from the others.Verification / Alternative check:Factor 225 = 3^2 * 5^2; its base (15) is composite.
Why Other Options Are Wrong:169, 289, and 361 are squares of primes, sharing the majority property.
Common Pitfalls:Overlooking the duplicate and ending with two “correct” entries; minimal repair ensures a single unambiguous answer.
Final Answer:225 is the square of a composite and is the odd number.