If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:10 am

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A. 5
B. 5(x-y)
C. 20x
D. 20y
E. 35x

Answer: C
Source: Manhattan prep

Key concept: If k is a divisor of n, then n/k is an INTEGER
For example, since 8 is a divisor of 24, it is also true that 24/8 is an integer
Likewise, since 14 is a divisor of 14, it is also true that 14/14 is an integer

The question asks, "Which of the following CANNOT be the greatest common divisor of 35x and 20y?"

C) If 20x is the greatest common divisor of 35x and 20y, then it must be true that 35x/20x and 20y/20x are INTEGERS
Notice that 20y/20x COULD be an integer if x is a divisor of y.
However, 35x/20x simplifies to be 7/4, which is definitely NOT an integer (regardless of the value of x)
As such, 20x can never be the greatest common divisor of 35x and 20y

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:10 am

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A. 5
B. 5(x-y)
C. 20x
D. 20y
E. 35x

Answer: C

Solution:

Since 20x is not a factor of 35x regardless of what x is, 20x can’t be the greatest common divisor of 35x and 20y.

Answer: C