Problem Solving

If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT
30x.
15y.
15(x + y).
15(x - y).
15,000.

According to me the answer should be 15y. Can someone tell me if its the right answer choice,However this question appeared in kaplan practice set 4 and I marked 15y and according to it , this was a wrong choice...

Let's check each choice
1) 30x/30x = Ok ; 15y/30x = 1/2(y/x); y=2,x=1. Ok
2) 30x/15y = 2(x/y). x=y=1. Possible. 15y/15y = 1. Ok
3) 30x/15(x+y) = 2x/x+y . x=2;y=2. Possible; 15y/15(x+y) = y/x+y; This is a fraction
4) 30x/15(x-y) = 2x/x-y . x=2;y=1. Possible; 15y/15(x-y) = y/x-y; x=2;y=1. Ok
5) 30x/15000 = 2x/1000. x=500. Possible; 15y/15000 = y/1000; Ok

Remember the other GCD problem we solved today?

30x=2*3*5*x
15y=3*5*y

GCD=3*5*unknown

(A)30x
if x was a factor of y
30x=2*3*5*x
15y=3*5*x*unknown. And if unknown equals 1 or any number not common to both then
GCD=2*3*5*x. Possible

(B)15y
if y was a factor of x
15y=3*5*y.
30x=2*3*5*y*unknown. And if unknown equals 1 or any number not common to both then
GCD=3*5y. Possible.

(E)15000. What if x and y have 1000 as a factor then
15y=3*5*1000*unknown
30x=2*3*5*1000*unknown And if unknown equals 1 or any number not common to both then
GCD=3*5*1000. Possible.

The contenders are either C or D. Will take me a while to figure this out.

hey sl750..

thanks for ur reply but why cant we consider x=y=1 in choice 3 then we will get 30*1/15*(1+1)=1 possible again..

Hey got it sl750..... thanks