What is the value of x^2 - y^2 ? (1) x - y = y + 2 (2) x - y = 1/(x+y)

Question

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

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

Bunuel · Answer

SOLUTION

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

(1) x - y = y + 2 --> x=2y+2, so x^2-y^2=(y+2)^2-y^2 --> to get the value of this expression we need to know the value of y. Not sufficient.

(2) x - y = 1/(x+y) --> cross-multiply: (x-y)(x+y)=1 --> x^2-y^2=1. Sufficient.

Answer: B.

beatthegmat05 · Answer

x^2-y^2 = (x-y)(x+y)

(1) x - y = y + 2
x^2-y^2 = (y + 2)(x+y) not sufficient

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

Correct answer is (B)

KSBGC · Answer

x^2 - y^2

( x + y) ( x - y)

Statement 1: x - y = y + 2. we don't know the value of x + y. perhaps it's not possible to determine the individual value of x and y .

Statement 2; x - y = 1/ x + y

cross multiplication gives us (x - y)( x + y) = 1. Sufficient.

The best answer is B.

dollytaneja51 · Answer

Statement 1 : x-y = y + 2 
x = 2y + 2
We need 1 more equation to find the value of x or y, without that we are not find the solution x^2 - y^2... Insufficient

Statement 2 : x-y = 1/(x+y)
(x-y) (x+y) = 1
x^2 - y^2 = 1
Sufficient

B is the correct answer.

Posted from my mobile device

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

The value of  x^2  –  y^2  has to be calculated.

Using the standard Algebraic identity of  a^2  –  b^2  = (a – b) (a + b).

Therefore, to calculate the value of  x^2  –  y^2 , we need information about (x – y) and (x + y)

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:  x - y = y + 2

Rearranging terms in the equation and solving, we have,

x – y – y = 2 OR

x = 2.

There is no information about y and therefore, the value of  x^2  –  y^2  cannot be calculated.
The data in statement 1 is insufficient to find the value of the expression.

Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2:  x - y =  \frac{1}{(x+y)}

Rearranging the terms of the equation, (x – y) (x + y) = 1.

Therefore,  x^2  –  y^2  = 1.

The data in statement 2 is sufficient to find the value of the expression.
Statement 2 alone is sufficient. Answer options C and E can be eliminated.

The correct answer option is B.

totaltestprepNick · Answer

B https://www.youtube.com/watch?v=wOaPthkGIls Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

What is the value of x^2 - y^2 ? (1) x - y = y + 2 (2) x - y = 1/(x+y)

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the value of x^2 - y^2 ? (1) x - y = y + 2 (2) x - y = 1/(x+y)

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards