Find the odd number: In 121, 88, 97, and 132, three are composite while one is prime. Identify the prime number.
Verbal Reasoning
Classification
Difficulty: Easy
Choose an option
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A121
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B88
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C97
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D132
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ENone of these
Answer
Correct Answer: 97
Explanation
Introduction / Context:Among mixed-sized integers, quickly separating primes from composites is key. Here, three numbers are composite; one is prime.
Given Data / Assumptions:
- Options: 121, 88, 97, 132.
- 121 = 11^2; 88 and 132 are even.
Concept / Approach:Use parity and perfect-square recognition, then check the remaining candidate with small primes.
Step-by-Step Solution:
121 = 11 * 11 → composite.88 → even and > 2 → composite.132 → even → composite.97 → not divisible by 2, 3, 5; test 7 and 11 quickly; none divide → prime.Verification / Alternative check:Upper bound for trial division is floor(sqrt(97)) = 9; primes to test: 2, 3, 5, 7. None divides 97, confirming primality.
Why Other Options Are Wrong:Each has an obvious factor: 121 is 11^2; 88 = 8 * 11; 132 = 12 * 11.
Common Pitfalls:Assuming “near 100” implies compositeness without checking.
Final Answer:97 is prime and therefore the odd number.