runningguy wrote:If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?
A) (x+z)/z
B) (y+z)/x
C) (x+y)/z
D) (xy)/z
E) (yz)/x
Note: To avoid confusion, I added some brackets to your answer choice.
Mitch already showed the approach of looking for values of x, y and z, such that we get a non-integer.
Here's another approach:
x is a multiple of z
So, we can say that
x = kz (for some integer k)
x is a factor of y
In other words, y is a multiple of x.
So, we can say that y = jx (for some integer j)
IMPORTANT: Since we already know that x = kz, let's replace x with kz to get:
y = jkz
So,
x = kz,
y = jkz and z = z.
Let's plug in these values to see what we get:
A) (x+z)/z = (
kz+z)/z = k+1 (= INTEGER)
B) (y+z)/x = (
jkz+z)/
kz = (jk+1)/k (not necessarily an integer)
C) (x+y)/z = (
kz+
jkz)/z = k+jk (= INTEGER)
D) (xy)/z = [(
kz)(
jkz)]/z = jk²z (= INTEGER)
E) (yz)/x = [(
jkz)(z)]/
kz = jz (= INTEGER)
Answer =
B
Cheers,
Brent
