Problem Solving

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

APPROACH A:
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

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

Since the greatest common divisor or greatest common factor (GCF) of any two positive integers must be no larger than the lesser of the two integers, the GCF can't be sum of the two integers. That is, the GCF of x and y can't be x + y.

Answer: E

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

Jeff's approach (recognizing that the GCD of two values cannot be greater than each value) is perfect.
However, if you didn't spot that, you can always use the Process of Elimination.

The question asks "Which of the following CANNOT be the greatest common divisor of x and y?"
So, if we can find values for x and y such that an answer choice CAN be the greatest common divisor of x and y, then we can ELIMINATE that answer choice

For example, if x = 3 and y = 2, then the GCD of x and y is 1
So, we can ELIMINATE A.
We can also ELIMINATE D since x - y = 3 - 2 = 1

Next, if x = 2 and y = 4, then the GCD of x and y is 2 (aka x)
So, we can ELIMINATE B.

Similarly, if x = 4 and y = 2, then the GCD of x and y is 2 (aka y)
So, we can ELIMINATE C.

By the process of elimination, the correct answer must be E

Cheers,
Brent