Bunuel
If x = y², what is the value of y – x?
(1) x = 4
(2) x + y = 2
Given: x = y² Target question: What is the value of y – x? Statement 1: x = 4 Plug this value into our given equation,
x = y², to get: 4 = y², which means EITHER y = 2 OR y = -2
Let's examine both cases:
Case a: If y = 2 and x = 4, then the answer to the target question is
y - x = 2 - 4 = -2Case b: If y = -2 and x = 4, then the answer to the target question is
y - x = (-2) - 4 = -6Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x + y = 2Subtract with y from both sides of the equation to get: x = 2 - y
Now take
x = y² and replace x with 2 - y to get: 2 - y = y²
Set this equation to zero to get: y² + y - 2 = 0
Factor: (y + 2)(y - 1) = 0
So, EITHER y = 2 OR y = 1
Case a: If y = 2, then x = 4 (since it's given that
x = y²). So, the answer to the target question is
y - x = 2 - 4 = -2Case b: If y = 1, then x = 1 (since it's given that
x = y²). So, the answer to the target question is
y - x = 1 - 1 = 0Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that EITHER y = 2 OR y = -2
Statement 2 tells us that EITHER y = 2 OR y = 1
When we combine the statements, we can see that it
MUST be the case that y = 2
If y = 2, then x = 4 (since it's given that
x = y²). So, the answer to the target question is
y - x = 2 - 4 = -2Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent