this can be easily understood as:
1.take any two prime nos. say 2, 3
then G.C.D - 1
2. take x=2;y=6
G.C.D.- 2=x
3.similarly G.C.D y
4.take x=6;y=4
G.C.D.=2(x-y)
so,G.C.D. can't be x+y
or likewise you can understand as G.C.D. is the highest COMMON factors b/w two nos. so their sum can't be so

sachin_yadav wrote:Hi All,

Please help. Don't know how answer is E.

Which of the following CANNOT be the greatest common divisor of two positive integers x and y ?

(A) 1
(B) x
(C) y
(D) x - y
(E) x + Y

Thanks & Regards
Sachin

The only information we have about x and y is that they're positive integers, so there will be very few conclusions we can draw about their greatest common factor.

However, here's one thing we do know: the greatest common factor of any positive integer is the integer itself.

Accordingly, there's no way that (x+y), which is greater than each of x and y, could be the greatest common factor of x and y.

Thank you so much. Really appreciate for your help.

Thanks & Regards
Sachin