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

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.

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.

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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.

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