If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?  Select:
A) 5
B) 5(x – y)
C) 20x
D) 20y
E) 35x
Looking at the list of answer choices, there are some that we can quickly eliminate...   IF   X = 1   Y = 1   Then we have 35 and 20, so the GCD = 5   Eliminate A.   X = 20   Y = 1   Then we have 700 and 20, so the GCD = 20   Eliminate D.   X = 1   Y = 35   Then we have 35 and 700, so the GCD = 35   Eliminate E.   With the remaining 2 answers, we have to think a little more.   To get a simple example of 5(X-Y) to be the GCD, we probably need 35X to be ODD   IF...   X = 3   Y = 2   Then we have 105 and 40, so the GCD = 5   5(X-Y) = 5(3-2) = 5   This can ALSO be the GCD   Eliminate B.   ANSWER:20x
<result>C</result>
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?