What is the value of x ?

[BTGmoderatorDC]

What is the value of x ?

(1) (x^2) + (y^2) = 25
(2) xy = 12

OA E

Source: GMAT Prep

[GMATGuruNY]

What is the value of x ?

(1) (x^2) + (y^2) = 25
(2) xy = 12

Both statements are satisfied by the following cases:
Case 1: x=3 and y=4
Case 2: x=4 and y=3
Since x can be different values, the two statement combined are INSUFFICIENT.

The correct answer is E.

[swerve]

1) \(x^2 + y^2 = 25\)
\(x\) can take multiple values. Eg: \(x=3, y=4\) OR \(x=4, y=3\) OR \(x=-3, y=4\) and so on. \(x\) and \(y\) can both take positive as well as negative values also. Insufficient. \(\Large{\color{red}\times}\)

2) \(xy = 12\)
Here also \(x\) can take multiple values. Eg: \(x=4, y=3\) Or \(x=-4, y=-3\). \(x\) and \(y\) can take mutliple values, though both \(x/y\) will have same sign. Insufficient. \(\Large{\color{red}\times}\)

Combining the two statements, \(x/y\) both have same sign, but still more than one cases possible. Eg, \(x=4, y=3\) OR \(x=-4, y=-3\) etc. Insufficient. \(\Large{\color{red}\times}\)

Therefore, __E__ \(\Large{\color{green}\checkmark}\)