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

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Difficulty:   35% (medium)

Question Stats: 66% (01:26) correct 34% (01:21) wrong based on 356 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

Originally posted by chintzzz on 19 Jun 2010, 02:31.
Last edited by Bunuel on 03 Jul 2013, 00:54, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
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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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GMAT Club Legend  V
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Posts: 4151
Re: If n is an integer, which of the following CANNOT be  [#permalink]

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

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

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A simple but effective method in solving this question would be to plug in simple values for n and eliminate options which can be factors of 3n + 4. It can also be a very efficient method to save time.

If n = 0, then 4 can be a factor of 3*0 + 4. Option A can be eliminated.

If n = 1, 7 can be a factor of 3*1 + 4. Option D can be eliminated.

If n = 2, 5 can be a factor of 3*2 + 4. Option B can be eliminated.

If n = 4, 8 can be a factor of 3*4 + 4. Option E can be eliminated.

The option left is C. It has to be the right answer.

Note: Remember to use the PEMDAS rule when you are evaluating the expression after plugging in values.

Hope this helps!
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Posts: 3158
Re: If n is an integer, which of the following CANNOT be  [#permalink]

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Solution

Approach and Working out

If 3n+4 is divisible by a number, then that number will be the factor of 3n+4.
Now, 3n +4 = 3(n+1) +3 = 3k +1
And, 3k+1 will never be divisible by 3 or by any multiple of 3.
In options, only multiple of 3 is 6.
Hence, 6 will never be a factor of 3n+4.

Thus, option C is the correct answer.
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Re: If n is an integer, which of the following CANNOT be  [#permalink]

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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

Since 3n + 4 will never be a multiple of 3, it will never be a multiple of 6. In other words, 6 cannot be a factor of 3n + 4.

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