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Re: If x and y are positive integers, each of the following [#permalink]
29 Nov 2013, 12:41

1

This post received KUDOS

Expert's post

nechets wrote:

Fantastic Bunuel, great catch.

Is it the case that x/(x+y) or y/(x+y) will never be integer? Is this the right way to elimate C algebraically? Or how would you do so?

Bunuel wrote:

nechets wrote:

Wait a minute, picking numbers:

If x= 1 and y =1 , both positive integers, why this could not be the base case for C?

If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT

A. 30x. B. 15y. C. 15(x + y). D. 15(x - y). E. 15,000.

If x=1 and y=1, then 30x=30 and 15y=15. The GCD of 30 and 15 is 15, while (C) gives 15(x+y)=30.

Hope it's clear.

Both x and y are positive integers, thus \(\frac{15y}{15(x+y)}=\frac{y}{x+y}\neq{integer}\) because the denominator is greater than the numerator. Thus 15(x+y) cannot be a divisor of 15y.

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