Choose the odd number: 27, 64, and 125 are perfect cubes (3^3, 4^3, 5^3). One number is not a perfect cube. Identify the non-cube.
Verbal Reasoning
Classification
Difficulty: Easy
Choose an option
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A27
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B64
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C125
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D384
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ENone of these
Answer
Correct Answer: 384
Explanation
Introduction / Context:Recognizing perfect cubes is a common categorization task.
Given Data / Assumptions:
- 27 = 3^3, 64 = 4^3, 125 = 5^3.
- 384 = ?
Concept / Approach:Compare each entry to nearby cubes or factorize to check whether all prime exponents are multiples of 3.
Step-by-Step Solution:
27 → perfect cube.64 → perfect cube.125 → perfect cube.384 = 2^7 * 3 (not all exponents multiples of 3) → not a cube.Verification / Alternative check:Locate 7^3 = 343 and 8^3 = 512; 384 lies between them and is neither.
Why Other Options Are Wrong:They equal exact cubes.
Common Pitfalls:Assuming “even and large” implies a cube; exact equality to n^3 is required.
Final Answer:384 is the non-cube.