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

Question

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

BrentGMATPrepNow · Accepted Answer

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

Answer: C

Cheers,
Brent

Bunuel · Answer

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.

Answer: C.

BrentGMATPrepNow · Answer

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

CrackverbalGMAT · Answer

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!

EgmatQuantExpert · Answer

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.
  Correct Answer: Option C

ScottTargetTestPrep · Answer

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.

Answer: C

Hoozan · Answer

Similar Question: https://gmatclub.com/forum/if-the-tens- ... 28744.html

Abhishek009 · Answer

If  n = 0  ,  3n +4 = 4 , DIvisible by  (A) 4 
If  n = 1  ,  3n +4 = 4 , DIvisible by  (D) 7 
If  n = 2  ,  3n +4 = 4 , DIvisible by  (B) 5 
If  n = 4  ,  3n +4 = 4  , DIvisible by  (E) 8  &  (A)

We are left with (C),answer!

orangebicycle5 · Answer

3n restricts us to n being a multiple of 3. Thus 6 can not be an answer choice.

Multiple + Multiple = Multiple
Non-Multiple + Multiple = Non-Multiple
Non-Multiple + Non-Multiple = ?

Aboyhasnoname · Answer

I did it by plugging in values. But the concept learning here... 
3n..could be or couldn't be divisble by 6.....if it is not divisible by 6....but divisible by 3..so we need 3 more to make it divisble by 6...but we are only getting 4 more.... 
if 3n is divisible by 6..then we need 6 more for it to be divisible by 6.. but we are only getting 4 more..so it wont be divisible by 6...

Alternatively... as mentioned in other explanations.. 
for a number to be divisible by 6 it has to be divisible by 3...but 3n+4 can never be divisible by 3 as we are moving 1 forward after 3n+3...

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

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GMAT Problem Solving (PS) Questions

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

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