What is the value of x^2 – y^2 ?

Question

What is the value of x^2 – y^2 ?
 
(1) x + y = 2y – 1 
(2) 5x - 5y = 1/(2x + 2y)

chipsy · Answer

We need to find x^2 - y^2 = (x-y) (x+y)

(A) x - y = -1 , Not suff.

(B) 5x - 5y = 1/(2x + 2y)

5 (x-y) * 2(x+y) = 1
 10 (x-y) (x+y) =1
 (x-y) (x+y) = 1/10
Sufficient.

answer is Option B.

Nikkb · Answer

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

1) x+y=2y-1
=> x-y=-1
even if we multiply both => (x+y)(x-y)= -(2y-1)

Not sufficient

2)5x - 5y = 1/(2x + 2y) 
=> 5(x-y) =1/(2x + 2y)
=> 5(x-y) *(2x + 2y)=1
=>5(x-y)*2(x+y)=1
> (x-y)(x+y)=1/10

Sufficient
 
Answer: B

BrentGMATPrepNow · Answer

Target question :    What is the value of x² – y² ?

Statement 1 : x + y = 2y – 1   
Subtract 2y from both sides to get: x - y = -1
There are several values of x and y that satisfy statement 1. Here are two: 
 Case a : x = 0 and y = 1, in which case  x² – y² = 0² – 1² = 0 - 1 = -1  
 Case b : x = 1 and y = 2, in which case  x² – y² = 1² – 2² = 1 - 4 = -3  
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : 5x - 5y = 1/(2x + 2y)  
Multiply both sides of the equation by (2x + 2y) to get: ( 2x + 2y )( 5x - 5y ) = 1

ASIDE: If you recognize that x² – y² = (x+y)(x-y), then you'll see that we're well on our way to answering the  target question

Rewrite as:  (2)(x + y)  (5)(x - y)  = 1
Or we can write: (2)(5) (x + y)(x - y)  = 1
Simplify: (10)( x² – y² ) = 1
Divide both sides by 10 to get:  x² – y² = 1/10 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer:  B

Cheers,
Brent

PK32 · Answer

By using statement 1 we can deduce (x+y)(x-y)= (2y-1) ;"Y" is still unknown.

By using statement 2 we can find (x+y)(x-y)= 1/10

so Answer is "B"

Solenja · Answer

hey chipsy in option B the 3 step, i think mathematical it is not correct

What is the value of x^2 – y^2 ?

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 ?

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