gcd(30x,15y)= 15*gcd(2x,y). Clearly values in option a and b can be attained if 2x=y.nobazinga wrote: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
Answer is C
Also, 15,000 is possible as gcd(2x,y) can very well be equal to 1,000.
Option d is also possible. let's say if you take x=2y, then 15*gcd(2x,y)= 15y*gcd(4,1)=15y=15(x-y)
Option c is wrong because it contradicts the fact that gcd of a set of numbers can never be greater than any of the individual numbers, more so because both the numbers given here are positive.
Since 15(x + y) is always greater than 15y for positive x, hence option C is the right ans.
