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If n is an integer, which of the following CANNOT be

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Joined: 16 Jun 2010
Posts: 18
If n is an integer, which of the following CANNOT be [#permalink]

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19 Jun 2010, 02:31
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Jul 2013, 00:54, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 44373

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19 Jun 2010, 02:43
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chintzzz 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.

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Re: If n is an integer, which of the following CANNOT be [#permalink]

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21 Nov 2017, 10:04
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chintzzz 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

KEY CONCEPTS
If a number is divisible by 6 it MUST also be divisible by 3
Conversely, if a number is NOT divisible by 3, then that number is NOT divisible by 6

3n + 4 = 3n + 3 + 1
= 3(n + 1) + 1
We can see that 3n+4 is 1 greater than some multiple of 3
This tells us that 3n+4 is NOT divisible by 3
This means (from the rules above) that 3n+4 is NOT divisible by 6

Cheers,
Brent
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Brent Hanneson – Founder of gmatprepnow.com

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Re: If n is an integer, which of the following CANNOT be [#permalink]

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21 Nov 2017, 10:09
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chintzzz 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

Another approach is to plug in integer values for n and start ELIMINATING answer choices..

Try n = 0
So, 3n + 4 = 3(0) + 4 = 4
4 IS a factor of 4
ELIMINATE A

Try n = 1
So, 3n + 4 = 3(1) + 4 = 7
7 IS a factor of 7
ELIMINATE D

Try n = 2
So, 3n + 4 = 3(2) + 4 = 10
5 IS a factor of 10
ELIMINATE B

Try n = 3
So, 3n + 4 = 3(3) + 4 = 13
Doesn't help...

Try n = 4
So, 3n + 4 = 3(4) + 4 = 16
8 IS a factor of 16
ELIMINATE E

By the process of elimination, the correct answer is C

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Re: If n is an integer, which of the following CANNOT be   [#permalink] 21 Nov 2017, 10:09
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