BTGmoderatorDC wrote:If 2xy + z = 9, what is the value of the positive integer z?
(1) xyz - z² = 0
(2) x + y - 3z = -5
Given: 2xy + z = 9
Target question: What is the value of the positive integer z?
Statement 1: xyz - z² = 0
Factor to get: z(xy - z) = 0
This means that EITHER z = 0 OR xy - z = 0
HOWEVER, we're told that z is a POSITIVE integer, which means z ≠0
So, it must be the case that
xy - z = 0
We know have:
2xy + z = 9
xy - z = 0
Multiply both sides of the bottom equation to get:
2xy + z = 9
2xy - 2z = 0
Subtract the bottom equation from the top equation to get: 3z = 9, which means
z = 3
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x + y - 3z = -5
We also know that
2xy + z = 9
ASIDE: for statement 1, I was able to eliminate the x and y variables, because they appeared together in the terms 2xy and xy
In statement 2, we aren't as lucky.
As such, this system of 2 equations and 3 variables in not enough information to solve for z.
Statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
