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Question

If n(n2−1) is divisible by 24, then which of the following statements is true?

A
n can be any odd integral value.
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B
n can be any integral value.
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C
n can be any even integral value.
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D
n can be any rational number.
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Solution

The correct option is A n can be any odd integral value.
n(n21)=n(n1)(n+1)
If n is even, then n1 and n+1 will be odd, therefore n(n21) is not divisible by 4 and therefore not divisible by 24.
Hence n has to be an odd integer.

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