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If a is a positive integer, then which of the following must : Multiple-choice Questions — Select One or More Answer Choices

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Re: If a is a positive integer, then which of the following must [#permalink]
N consecutive numbers are always divisible by factors of N!
3 consecutive numbers is always divisibly by factors of 3! --> {1, 2, 3, 6}. So its non prime as it is divisible by more than 2 factors already

Option C and E
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If a is a positive integer, then which of the following must [#permalink]
rubytuesdays21 wrote:
It's important to note that we know it is divisible by 3 because (a-1)(a)(a+1) represents three consecutive integers. Since the question states it is a positive integer, we know that it will always result in a multiple of 3.


To expand on this, if we write out possibilities, we see groupings of: [0*1*2], [1*2*3], [2*3*4], [7*8*9], ...

Since there are 3 terms, a multiple of 3 will always be in those groupings, because multiples of 3 only have 2 integers between them. So, one of the three numbers has to be a multiple of 3.

It may seem like an exception is [0*1*2]. But 0 is a multiple of every number, including 3.
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If a is a positive integer, then which of the following must [#permalink]
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