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Re: If x and y are positive, what is the value of x-y?
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30 Apr 2012, 11:22

eybrj2 wrote:

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

(1) (x^2 - y^2)/ (x + y) = 4

(2) x + y = 7

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

Re: If x and y are positive, what is the value of x-y?
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16 Oct 2017, 07:35

Top Contributor

eybrj2 wrote:

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

(1) (x^2 - y^2)/ (x + y) = 4

(2) x + y = 7

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