Bunuel
What is the value of x^2 – y^2 ?
(1) x + y = 2y – 1
(2) 5x - 5y = 1/(2x + 2y)
Target question: What is the value of x² – y² ? Statement 1: x + y = 2y – 1 Subtract 2y from both sides to get: x - y = -1
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 1, in which case
x² – y² = 0² – 1² = 0 - 1 = -1 Case b: x = 1 and y = 2, in which case
x² – y² = 1² – 2² = 1 - 4 = -3 Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 5x - 5y = 1/(2x + 2y) Multiply both sides of the equation by (2x + 2y) to get: (
2x + 2y)(
5x - 5y) = 1
ASIDE: If you recognize that x² – y² = (x+y)(x-y), then you'll see that we're well on our way to answering the
target questionRewrite as:
(2)(x + y)(5)(x - y) = 1
Or we can write: (2)(5)
(x + y)(x - y) = 1
Simplify: (10)(
x² – y²) = 1
Divide both sides by 10 to get:
x² – y² = 1/10Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer:
Cheers,
Brent