Number set — pick the odd number out (all others are composite): 4, 6, 8, 9, 10, 11, 12
Aptitude
Odd Man Out and Series
Difficulty: Easy
Choose an option
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A10
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B11
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C12
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D9
Answer
Correct Answer: 11
Explanation
Introduction / Context:This is a property-based odd-one-out question. The simplest distinguishing feature among the listed integers is “prime vs. composite.” Identify the only prime to find the outlier.
Given Data / Assumptions:
- Numbers: 4, 6, 8, 9, 10, 11, 12
- Exactly one should be different by a basic number-theory property.
Concept / Approach:Check primality. A prime has exactly two positive divisors (1 and itself). Composite numbers have more than two factors. Quickly factor each number to classify it.
Step-by-Step Solution:
4 = 22 → composite6 = 23 → composite8 = 222 → composite9 = 33 → composite10 = 25 → composite11 → prime (only 1 and 11 divide 11)12 = 223 → compositeThus 11 is the only prime; all others are composite.Verification / Alternative check:
Try any divisibility tests: 11 is not divisible by 2, 3, 5; hence prime in this range.Why Other Options Are Wrong:
4, 6, 8, 9, 10, 12 each has nontrivial factors; none is prime.Common Pitfalls:
Mistaking 9 (a perfect square) for prime — it is composite (3*3).Final Answer:11