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If a is a positive integer, then which of the following must
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06 Aug 2017, 12:37

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If a is a positive integer, then which of the following must be true of (a − 1)(a)(a + 1)?

Indicate all that apply.

❑ It is always positive.

❑ It is always odd.

❑ It is always divisible by 3.

❑ It is always divisible by 4.

❑ It is non-prime.

Re: If a is a positive integer, then which of the following must
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24 Sep 2017, 07:31

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Let's check the answers one by one

❑ It is always positive: if n = 1, then we have 0*1*2 = 0 and 0 is neither positive nor negative

❑ It is always odd: if n = 2, then we have 1*2*3 = 6 and 6 is even

❑ It is always divisible by 3: if we start with n = 1, we get 0 that is divisible for every number, then if n=1, we get 6, if n=2, we get 24, if n=3, we get 60 and so on

❑ It is always divisible by 4: if n = 2, then we have 6 as before and 6 is not divisible by 4

❑ It is non-prime: same argument as for "divisible by 3", the result is never prime.

Thus the answers are C and E

❑ It is always positive: if n = 1, then we have 0*1*2 = 0 and 0 is neither positive nor negative

❑ It is always odd: if n = 2, then we have 1*2*3 = 6 and 6 is even

❑ It is always divisible by 3: if we start with n = 1, we get 0 that is divisible for every number, then if n=1, we get 6, if n=2, we get 24, if n=3, we get 60 and so on

❑ It is always divisible by 4: if n = 2, then we have 6 as before and 6 is not divisible by 4

❑ It is non-prime: same argument as for "divisible by 3", the result is never prime.

Thus the answers are C and E

Re: If a is a positive integer, then which of the following must
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26 Jul 2021, 10:55

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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.

Re: If a is a positive integer, then which of the following must
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05 Apr 2023, 19:35

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

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

If a is a positive integer, then which of the following must
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27 Dec 2023, 13:40

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.

gmatclubot

If a is a positive integer, then which of the following must [#permalink]

27 Dec 2023, 13:40
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