sana.noor wrote:What is the value of xy?
1) (x+y)^2 =37
2) (x-y)^2 =17

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Target question: What is the value of xy?

Statement 1: (x+y)^2 =37
This tells us that x+y = -sqrt37 or x+y = sqrt37
There are several possible values of x and y that satisfy this condition.
So, statement 1 is NOT SUFFICIENT

Statement 2: (x-y)^2 =17
This tells us that x-y = -sqrt17 or x-y = sqrt17
There are several possible values of x and y that satisfy this condition.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
1. (x+y)^2 =37
2. (x-y)^2 =17

Expand the left-hand-side of both equations to get:
1. x^2 + 2xy + y^2 = 37
2. x^2 - 2xy + y^2 = 17

Subtract equation #2 from equation #1 to get:
4xy = 20, which means xy must equal 5
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

sana.noor wrote:thanku soo much brent,....i have one more question regarding square root...while taking square we do consider +ve and -ve signs but why we consider -ve signs when taking square root?? i read somewhere that we always consider positive value of square root of any number.

To answer that question, consider these two equations

#1. x^2 = 9
#2. x = sqrt(9)

A lot of students treat these as identical equations, but they are not.

Equation #1 has two solutions: x=3 and x=-3, since 3^2 = 9 and since (-3)^2 = 9

Equation #2 is different. By definition, the sqrt notation dictates that we find the positive value that, when squared, equals the value inside the root sign. So, if x = sqrt(9), then x =3

From the Official Guide:
Every positive number n has two square roots, one positive and the other negative, but sqrt(n) denotes the positive number whose square is n.

Cheers,
Brent