Carcass wrote:
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
Key concept: Each divisor of integer N is less than or equal to N For example, here are the divisors of 15: {1, 3, 5, 15}
Notice that every divisor is less than or equal to 15.
Similarly, if a number is a divisor of both x AND y, then that number must be less than or equal to x AND less than or equal to y.
As such, the greatest common divisor of x and y cannot be greater than both x and y
Since (x + y) > x and (x + y) > y, we can conclude that x+y cannot be the greatest common divisor of x and y.
Answer: E
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep