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SC Moderator V
Joined: 25 Sep 2018
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Concentration: Finance, Strategy
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If a is an integer greater than zero, then a(a + 1)(a + 3) is  [#permalink]

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Difficulty:   15% (low)

Question Stats: 82% (01:41) correct 18% (01:29) wrong based on 117 sessions

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If a is an integer greater than zero, then a(a + 1)(a + 3) is

A) Even only when a is even
B) Even only when a is odd
C) odd whenever a is odd
D) Divisible by 3 only when a is odd
E) Divisible by 4 whenever a is odd

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Originally posted by Abhi077 on 26 Sep 2018, 11:44.
Last edited by Bunuel on 26 Sep 2018, 11:50, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Aug 2009
Posts: 8753
Re: If a is an integer greater than zero, then a(a + 1)(a + 3) is  [#permalink]

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Abhi077 wrote:
If a is an integer greater than zero, then a(a + 1)(a + 3) is

A) Even only when a is even
B) Even only when a is odd
C) odd whenever a is odd
D) Divisible by 3 only when a is odd
E) Divisible by 4 whenever a is odd

Now a and a+1 are consecutive integers, so the product a(a+1)(a+3) will always be even..
Choices A,B and C are out

Now, a, a+1, a+2, a+3 are 4 consecutive integers, so one of them is surely a multiple of 3..
If a is a multiple of 3, the product will also be a multiple of 3.. but X can be 3 or 6 too
So eliminate D

Ans is E
Let's see
When a is ODD a+1and a+3 both will be even , so the product will be a multiple of 4... Rather a multiple of atleast 8
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Re: If a is an integer greater than zero, then a(a + 1)(a + 3) is  [#permalink]

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Abhi077 wrote:
If a is an integer greater than zero, then a(a + 1)(a + 3) is

A) Even only when a is even
B) Even only when a is odd
C) odd whenever a is odd
D) Divisible by 3 only when a is odd
E) Divisible by 4 whenever a is odd

This is a copy of the following OG question: https://gmatclub.com/forum/if-n-is-a-po ... 16251.html
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Re: If a is an integer greater than zero, then a(a + 1)(a + 3) is  [#permalink]

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_________________ Re: If a is an integer greater than zero, then a(a + 1)(a + 3) is   [#permalink] 05 May 2020, 23:26

# If a is an integer greater than zero, then a(a + 1)(a + 3) is  