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

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If n is an integer, which of the following CANNOT be a [#permalink] New post 24 Jan 2005, 19:29
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
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 [#permalink] New post 24 Jan 2005, 19:35
Answer = C

I just used POE with a range of values of n
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 [#permalink] New post 24 Jan 2005, 19:38
B

if n=5, then 3n+4=19 a prime number! cannot be a factor other than 1 and itself.
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 [#permalink] New post 24 Jan 2005, 19:42
But if n = 2 then 3n + 4 = 10 so 5 is a factor of 10
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 [#permalink] New post 24 Jan 2005, 19:43
I am not sure we can come up with a general way of solving such problems.
Here are two ways for solving this problem.
1) Try various values of n,
2) We can see that 3n +4 will not be a multiple of 3. This means it will not be a multiple of 6 as any number not divisible by 3 is not divisible by 6.
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 [#permalink] New post 24 Jan 2005, 21:22
3n+4=3(n+1)+1
Therefore 3 cannot be a factor of it. Neither 6.

Therefore C.
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 [#permalink] New post 24 Jan 2005, 21:33
HongHu wrote:
3n+4=3(n+1)+1
Therefore 3 cannot be a factor of it. Neither 6.

Therefore C.

thats a good way of doing..
  [#permalink] 24 Jan 2005, 21:33
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