If 0 < x < y, What Is The Value Of (x+y)^2/(x−y)^2? GMAT Data Sufficiency

Question: If 0 < x < y, what is the value of (x+y)^2/(x−y)^2?
(1) x^2+y^2=3xy
(2) xy = 3

1. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
2. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

‘If 0 < x < y, what is the value of (x+y)^2/(x−y)^2?' – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken f0rom the book "GMAT Quantitative Review".
The GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:

There is only one approach solution to this problem.
Given to us are two variables x and y, which are related to each other as 0 < x< y
It has asked to calculate the value of \((x+y)^2\)/\((x-y)^2\).
We are given two statements and we are required to check whether these two statements are sufficient to get the answer.
In the first statement, it is given that,

1. x^2+y^2=3xy

We have,
\((x+y)^2\)/\((x-y)^2\) =\((x+y)^2\)/ \((x-y)^2\) = (\(x^2\)+ \(y^2\) + 2xy) / (\(x^2\)+\(y^2\)- 2xy)
= (\(x^2\)+ \(y^2\)+ 2xy) / (\(x^2\)+\(y^2\)- 2xy)
Putting the value of \(x^2\)+ \(y^2\)= 3xy
= (3xy +2xy) / (3xy-2xy)
= 5xy / xy = 5
The value of \((x+y)^2\)/\((x-y)^2\) is 5.
Therefore this statement is sufficient to get the answer.
In the second statement it is given that ,

2. Xy = 3

We have,
\((x+y)^2\)/\((x-y)^2\) = (\(x^2\)+ \(y^2\)+ 2xy) / (\(x^2\)+\(y^2\)- 2xy)
Putting the value of xy in the equation.
= (\(x^2\)+ \(y^2\)+ 2.3) / (\(x^2\)+\(y^2\)- 2.3)
This equation cannot be further solved.
Therefore this statement is not sufficient to get the answer.
So the correct option will be option A.

Correct Answer: A

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