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

1

Expert Reply

Question Stats:

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.

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

1

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
[#permalink]
26 Jul 2021, 10:55

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.

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