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

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Director
Joined: 21 Sep 2004
Posts: 618
Followers: 1

Kudos [?]: 5 [0], given: 0

If n is an integer, which of the following CANNOT be a [#permalink]  24 Jan 2005, 18:29
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
Director
Joined: 07 Jun 2004
Posts: 618
Location: PA
Followers: 3

Kudos [?]: 218 [0], given: 22

I just used POE with a range of values of n
Current Student
Joined: 28 Dec 2004
Posts: 3395
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 175 [0], given: 2

B

if n=5, then 3n+4=19 a prime number! cannot be a factor other than 1 and itself.
Director
Joined: 07 Jun 2004
Posts: 618
Location: PA
Followers: 3

Kudos [?]: 218 [0], given: 22

But if n = 2 then 3n + 4 = 10 so 5 is a factor of 10
Director
Joined: 19 Nov 2004
Posts: 565
Location: SF Bay Area, USA
Followers: 3

Kudos [?]: 44 [0], given: 0

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.
SVP
Joined: 03 Jan 2005
Posts: 2251
Followers: 13

Kudos [?]: 210 [0], given: 0

3n+4=3(n+1)+1
Therefore 3 cannot be a factor of it. Neither 6.

Therefore C.
Director
Joined: 21 Sep 2004
Posts: 618
Followers: 1

Kudos [?]: 5 [0], given: 0

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..
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