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metallicafan
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If S = y^2 + 2xy + x^2, what is the value of xy?
(1) x + y = 1
(2) S = 1
My approach:
(1) x + y = 1
Scenario A: x= 0.6 and y= 0.4, xy=0.24
Scenario B: x= 0.8 and y= 0.2, xy=0.16
INSUFFICIENT
(2) S = 1
1 = y^2 + 2xy + x^2
1 = (x+y)^2
Unsquaring:
1 = square root of (x+y)^2
Then:
1 = |x+y|
So:
x+ y = 1 OR x+y = -1
It happens the same as in scenarios A and B.
INSUFFICIENT.
(1) and (2) INSUFFICIENT
However, is there a faster way to solve it? This approach is exahusting!
OA: E
(1) x + y = 1
(2) S = 1
My approach:
(1) x + y = 1
Scenario A: x= 0.6 and y= 0.4, xy=0.24
Scenario B: x= 0.8 and y= 0.2, xy=0.16
INSUFFICIENT
(2) S = 1
1 = y^2 + 2xy + x^2
1 = (x+y)^2
Unsquaring:
1 = square root of (x+y)^2
Then:
1 = |x+y|
So:
x+ y = 1 OR x+y = -1
It happens the same as in scenarios A and B.
INSUFFICIENT.
(1) and (2) INSUFFICIENT
However, is there a faster way to solve it? This approach is exahusting!
OA: E
