If x + y = 2 and x^2 + y^2 = 2, What is the Value of xy? GMAT Problem Solving

Question: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

1. –2
2. –1
3. 0
4. 1
5. 2

Correct Answer: D
Solution and Explanation:
Approach Solution 1:
We have an equation (x+y)^2= x^2+y^2+2xy -> (1)

The question stem has given the following details:
x+y= 2
x^2+y^2=2 -> (2)

Because x+y= 2, value of (x+y)^2= 2^2= 4 -> (3)

Substituting values from (2) and (3) in equation (1)
(x+y)^2= x^2+y^2+2xy
4= 2 + 2xy
2xy= 4-2= 2

Therefore, xy= 2/2= 1

Approach Solution 2:
Given
(x+Y) = 2 and X^2 + Y^2= 2
(x+Y) = 2

Squaring both sides.

X^2 + Y^2 + 2xy = 4
2 + 2xy = 4

Solving for xy = 1

Approach Solution 3:
It is based on an algebraic formula..
(X+y)^2=x^2+y^2+2xy..
Substitute the values given..
2^2=2+2xy…
2xy=4-2=2.... xy= 1

“If x + y = 2 and x^2 + y^2 = 2, what is the value of xy?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2018 Quantitative Review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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