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
a) 1
b) x
c) y
d) x-y
e) x + y
APPROACH A:cpay3245 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
We'll solve this by eliminating the answer choices that CAN be greatest common divisor (GCD) of two positive integers x and y.
A) x = 2 and y = 3, which means the GCD = 1. ELIMINATE A
B) x = 2 and y = 4, which means the GCD = 2 = x. ELIMINATE B
C) x = 4 and y = 2, which means the GCD = 2 = y. ELIMINATE C
D) x = 3 and y = 2, which means the GCD = 1 = x-y. ELIMINATE D
By the process of elimination, the correct answer must be E
APPROACH B:
Recognize that the GCD of x and y must be less than or equal to x and less than or equal to y.
Since x + y is greater than x and y, it could never be the GCD of x and y.
Answer = E
Cheers,
Brent
