If x and y are positive, what is the value of x-y?

(1) (x^2 - y^2)/ (x + y) = 4 --> \(\frac{(x- y)(x+y)}{x + y}= 4\) --> reduce by \(x+y\): \(x-y=4\). Sufficient.

(2) x + y = 7. Clearly insufficient.

Answer: A.
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Ans Exp:

so we are required to find the difference between x and y


Statement 1: (x^2 - y^2)/ (x + y) = 4
by observing keenly we can get that the numerator i.e (x^2 - y^2) is in (a^2)-(b^2) so this can be written as
(a +b)(a-b) so

(x^2 - y^2)/ (x + y) = 4 => (x+y)(x-y)/(x+y)=4 =>by cancelling x+y in both numerator and denominator we are left with x-y=4 which is required ,so statement 1 is sufficient to answer the question .

Statement 2: x+y=7 as the question wanted us to solve for x-y we do nothing with x+y so statement 2 is insufficient


Answer = A.

A is correct!

(1) [x^2 - y^2]/(x+y) = 4 --> simplifies to (x-y) = 4

SUFFICIENT

(2) x+y = 7

NOT SUFFICIENT - we don't know anything about x-y from this

Target question: What is the value of x-y?

Given: x and y are positive

Statement 1: (x² - y²)/(x + y) = 4
Factor the numerator to get: (x - y)(x + y)/(x + y) = 4
Simplify: (x - y) = 4 PERFECT!
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x + y = 7
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 6 and y = 1, in which case x - y = 6 - 1 = 5
Case b: x = 5 and y = 2, in which case x - y = 5 - 2 = 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A
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