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What is the value of x^2 - y^2 ?

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What is the value of x^2 - y^2 ?

by M7MBA » Sat May 05, 2018 11:48 pm

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What is the value of x^2 - y^2 ?

(1) x - y = y + 2
(2) x - y = 1/(x+y)

The OA is the option B.

May someone helps me here? I don't know how to solve this DS question.
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by Vincen » Sun May 06, 2018 9:08 am

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Hello M7MBA.

We have to find the value of $$x^2-y^2 .$$

(1) x - y = y + 2

From this equation, we can derive x and substitute in the given expression and we will get: $$x-y=y+2\ \ \Rightarrow\ \ \ x=2y+2.$$ $$x^2-y^2=\left(2y+2\right)^2-y^2=4y^2+8y+4-y^2=3y^2+8y+4.$$ We cannot find the value of "y" from this last equation. Hence, we can't answer the original question. Therefore, this statement is NOT SUFFICIENT.

(2) x - y = 1/(x+y)

From this equation we will get the following: $$x-y=\frac{1}{x+y}$$ $$\Rightarrow\ \ \left(x-y\right)\left(x+y\right)=1$$ $$\Rightarrow\ \ x^2-y^2=1\ .$$ Therefore, we found an answer for the original question. Hence, this statement is SUFFICIENT.

In conclusion, the correct answer is the option B.
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by KCTester » Sun May 06, 2018 10:49 am

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There are two key things in play in this question:
1. Difference of squares where x^2 - y^2 = (x + y)(x - y)
2. In order to be able to solve equations with multiple variables, you need as many independent equations as you have variables so that you can express one of the variables in terms of another.

Our strategy for this question involves using point 1 in order to see if, with the additional information provided, we can get down to a case where we DO have the same number of independent equations as variables.

Statement 1:
Let's replace x - y with y + 2 and see what happens:
(x + y)(y + 2) = xy + 2x + y^2 + 2y
This is not helpful because we still have one equations, two variables, and no ability to assign value to anything.
NOT SUFFICIENT!

Statement 2:
Let's replace x - y with 1/(x + y):
(x + y) * (1/(x + y)) = 1 since x + y cancels out.
SUFFICIENT

Correct answer: B

A good takeaway from this question is that GMAT question writers love using the difference of squares, so if you spot in a question, then it's very likely that remembering that x^2 - y^2 = (x + y)(x - y) is going to be a key step on the way to a good approach.
contact KCTester:
[email protected]
Or check us out at:
https://testprepny.com/
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