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OG Quantative Review (Math reveiwbook question)

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OG Quantative Review (Math reveiwbook question)

by summertime » Tue Mar 31, 2009 6:08 pm
Hello:

I apologize in advance if this question has been asked before, but I am 6on question 125 in the GMAT Quantitative Reviewbook from the Official Guide.

It asks if x is an integer and y=3x+2, which of the following cannot be a divisor of y? 4,5,6,7,or 8. The answer is 6, but the explanation does not make sense to me.

Can someone please explain it?
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by Ian Stewart » Wed Apr 01, 2009 4:22 am
If x is an integer, then 3x is a multiple of 3. Multiples of 3 are separated by 3; if 3x is a multiple of 3, the nearest larger multiples of 3 are 3x+3, 3x+6, 3x+9, etc.

So 3x + 2 can't be a multiple of 3; indeed, because it is 2 more than a multiple of 3, the remainder will be 2 when 3x+2 is divided by 3. Since 3x+2 is not divisible by 3, it cannot possibly be divisible by 6, since every multiple of 6 must be a multiple of the divisors of 6.
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