Need help explaining an official answer explanation

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Problem:

1) If x is an integer and y=3x+2, which of the following cannot be a divisor of y?

A) 4
B) 5
C) 6
D) 7
E) 8

The official ans. explanation states that "Altough 3x is always divisible by 3, so 3x+2 cannot be div. by 3 since 2 is not divisible by 3. Thus, 3x+2 cannot be divisible by any multiple of 3, including 6." Though by that logic can't the test taker think to himself, well 2 cannot be divisble by 7 as well.

Brain is fried and perhaps I can't see the obvious here. Any help is much appreciated!

Thanks
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by bharathh » Sun Aug 30, 2009 11:03 am
Just plugged in numbers ... You can get the answer just taking a few numbers that y can be

x=0 and on to make things simple

y=2,5,8,11,14

From the above 5 numbers 4,5,7 and 8 are ruled out... leaving only 6

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phaedrus82 wrote:Problem:

1) If x is an integer and y=3x+2, which of the following cannot be a divisor of y?

A) 4
B) 5
C) 6
D) 7
E) 8

The official ans. explanation states that "Altough 3x is always divisible by 3, so 3x+2 cannot be div. by 3 since 2 is not divisible by 3. Thus, 3x+2 cannot be divisible by any multiple of 3, including 6." Though by that logic can't the test taker think to himself, well 2 cannot be divisble by 7 as well.

Brain is fried and perhaps I can't see the obvious here. Any help is much appreciated!

Thanks
when 3x divided by 6 will leave either 3 or 0 as remainder. 3x+2 will leave either 5 or 2 as remainder. Hence never divisible by 6

Thanks,
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