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# If n is an integer, which of the following CANNOT be a factor of 3n+4?

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VP
Joined: 03 Apr 2007
Posts: 1143
If n is an integer, which of the following CANNOT be a factor of 3n+4?  [#permalink]

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Updated on: 15 Apr 2015, 03:51
10
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Difficulty:

45% (medium)

Question Stats:

66% (01:40) correct 35% (01:27) wrong based on 200 sessions

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If n is an integer, which of the following CANNOT be a factor of 3n+4?

A. 4
B. 5
C. 6
D. 7
E. 8

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-an-integer-which-of-the-following-cannot-be-96084.html

Originally posted by goalsnr on 19 May 2008, 16:26.
Last edited by Bunuel on 15 Apr 2015, 03:51, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Director
Joined: 10 Sep 2007
Posts: 874
Re: If n is an integer, which of the following CANNOT be a factor of 3n+4?  [#permalink]

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19 May 2008, 16:54
2
2
It can never be equal to 6 because 6 is multiple of 3.
Here We have equation with Multiples of 3 added with 4.
All the even multiple of 3 will be multiple of 6 as well and we are adding 4 into them, so we can never achieve 6 as a factor for such cases.
For all the odd multiple of 3 you will need to add 3 to make it multiple of 6, but we are adding 4 so again 6 cannot be a factor.

We do not need to bother about other factors at all.
Senior Manager
Joined: 19 Apr 2008
Posts: 289
Re: If n is an integer, which of the following CANNOT be a factor of 3n+4?  [#permalink]

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19 May 2008, 16:57
2
goalsnr wrote:
16. If n is an integer, which of the following CANNOT be a factor of 3n + 4 ?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

I got thi s one correct by plugging in numbers and doing POE. Can you solve this in less than 1 minute?

I will try :
Looking at this, only 6 is multiple of 3 and since in term 3*n+4 , 4 is not a multiple of 3 ; 3n+4 can not ever be multiple of 6 . -----C
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Joined: 19 May 2008
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Location: Mumbai
Re: If n is an integer, which of the following CANNOT be a factor of 3n+4?  [#permalink]

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20 May 2008, 20:38
If POE is done, then 4,5,7 and 8 will eliminated and the answer would be 6.
Math Expert
Joined: 02 Sep 2009
Posts: 53716
Re: If n is an integer, which of the following CANNOT be a factor of 3n+4?  [#permalink]

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15 Apr 2015, 03:51
2
3
goalsnr wrote:
If n is an integer, which of the following CANNOT be a factor of 3n+4?

A. 4
B. 5
C. 6
D. 7
E. 8

$$3n+4=3(n+1)+1$$ cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 2*3=6 as well.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-an-integer-which-of-the-following-cannot-be-96084.html
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Re: If n is an integer, which of the following CANNOT be a factor of 3n+4?  [#permalink]

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17 Feb 2019, 11:41
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Re: If n is an integer, which of the following CANNOT be a factor of 3n+4?   [#permalink] 17 Feb 2019, 11:41
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# If n is an integer, which of the following CANNOT be a factor of 3n+4?

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