galaxis09 wrote:
If 0<x<y, what is the value of (x+y)^2 / (x-y)^2
(1) x^2 + y^2 = 3xy
(2) xy = 3
Target question:
What is the value of (x+y)^2 / (x-y)^2
If we expand the numerator and denominator, we get [x^2 + 2xy + y^2] / [x^2 - 2xy + y^2], so we can rephrase the target question.
Rephrased target question:
What is the value of [x^2 + 2xy + y^2] / [x^2 - 2xy + y^2]?
Statement 1: x^2 + y^2 = 3xy
Since x^2 + y^2 appears in the numerator and the denominator of the rephrased target question, we can replace x^2 + y^2 with
3xy to get:
What is the value of [
3xy + 2xy] / [
3xy - 2xy]?
This simplifies to be 5xy/xy, which equals 5 (since neither x nor y equal 0)
Since the expression evaluates to be
one distinct value, we can answer the
target question with certainty.
So statement 1 is SUFFICIENT
Statement 2: xy = 3
Since xy appears in the numerator and the denominator of the rephrased target question, we can replace xy with
3 to get:
What is the value of [x^2 + 2(
3) + y^2]/[x^2 - 2(
3) + y^2]?
This simplifies to be [x^2 + y^2 + 6]/[x^2 + y^2 - 6]
Can we simplify this expression further so that we get only one distinct value?
No.
The value of the expression can vary, depending on the values of x and y. To demonstrate this, consider these two case:
Case a: x=0.5, y=6 in which case
[x^2 + 2xy + y^2] / [x^2 - 2xy + y^2] = -13/11
Case b: x=1, y=3 in which case
[x^2 + 2xy + y^2] / [x^2 - 2xy + y^2] = -2
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
