Bunuel wrote:
If x = 300 − y − z, what is the value of x?
(1) y = (x + z)/2
(2) x = (y + z)/2
Given: x = 300 − y − z STRATEGY: In order to solve one of the equations below for x, I'll need to eliminate the variables y and z (and leave only x's).
So, I'm going to begin by solving the given equation for a variable other than x. Let's solve the equation for y by first adding y to both sides of the equation to get:
x + y = 300 − zNow subtract x from both sides of the equation:
y = 300 − z - xTarget question: What is the value of x? Statement 1: y = (x + z)/2Replace y with
300 − z - x to get:
300 − z - x = (x + z)/2 It appears that we still we're unable to eliminate the variable z. But to be extra safe, let's ensure that is the case.
First, multiply both sides of the equation by 2 to get:
600 − 2z - 2x = x + zAt this point, we can see that the variable z remains, which means there are infinitely many solutions to this linear equation.
As such, statement 1 is NOT SUFFICIENT
Statement 2: x = (y + z)/2Replace y with
300 − z - x to get:
x = (300 − z - x + z)/2Multiply both sides of the equation by 2 to get:
2x = 300 − z - x + zSimplify the right side:
2x = 300 - x Add x to both sides:
3x = 300 We can see that
x = 100Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent