Data Sufficiency

If 0<x<y, what is the value of (x+y)^2 / (x-y)^2

(1) x^2 + y^2 = 3xy

(2) xy = 3

Strongt 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

0<x<y,
(x+y)^2 / (x-y)^2........A)

1) x^2 + y^2 = 3xy;
x^2 + y^2-2xy = xy;
(x-y)^2=xy;
also x^2 + y^2 = 3xy;
x^2 + y^2+2xy = 3xy+2xy;
(x+y)^2=5xy;

substituting value of (x-y)^2 and (x+y)^2 in A) we have;
5xy/xy; 5; hence 1) is sufficient to answer the question.

2)xy=3;
x=3/y; substituting in A) we have (3/y+y)^2/(3/y-y)^2;
(3+y^2)^2/(3-y^2)^2; now we cannot solve this expression without additional information hence answer should be A

Thanks for your response,

I had to read your answer a couple of times before I fully understood your method.
I got this question right on the test( i guessed it) but this seems to be a very difficult question.
is there any easier way to deal with similar questions

Strongt wrote:Thanks for your response,

I had to read your answer a couple of times before I fully understood your method.
I got this question right on the test( i guessed it) but this seems to be a very difficult question.
is there any easier way to deal with similar questions

Hi!

manpsingh's approach is good, and perhaps easier to understand if we look at the information slightly differently.

If 0<x<y, what is the value of (x+y)^2 / (x-y)^2

(1) x^2 + y^2 = 3xy

(2) xy = 3

First, let's think about the question stem (always a good first step in DS).

We see that we have a perfect square on top and a perfect square on the bottom; however, there's no quick way to cancel out to simplify. So, we either need values for x and y or an expression that we can substitute in to both the numerator and the denominator.

(2) xy=3. There's no way that xy=3 is going to get rid of the x^2 and y^2 on the top and bottom of our fraction, so (2) is insufficient. If we get stuck on (1), at least we can eliminate B and D.

(1) x^2 + y^2 = 3xy

We already identified that we have two perfect squares which will contain an x^2 term, a y^2 term and an xy term, so (1) is looking much more promising than (2). Let's expand the original question:

What's the value of (x^2 + 2xy + y^2)/(x^2 - 2xy + y^2)?

Rearranging so that we can substitute in for x^2 + y^2:

What's the value of (x^2 + y^2 + 2xy)/(x^2 + y^2 - 2xy)?

Now we sub in "3xy" for "x^2 + y^2" on both top and bottom:

What's the value of (3xy + 2xy)/(3xy - 2xy)?

What's the value of (5xy)/(xy)?

What's the value of 5?

Well, the value of 5 is 5: sufficient!

(1) is sufficient, (2) isn't: choose (A)

Now, that might have seemed to be very time consuming, but if see that substitution is the way to go and are confident in your algebra, it's really only a 60-90 second solution.