Is x positive?
(1) |x^2| = 3

For sake of simplifying the calculation let us re frame the above eqn as |x^2|=4 ( it doesn't change the purpose )

The above eqn is true for both x= -2 and x=2

Hence Insufficient.

(2) |6 - 5y| = x

Since x is equated to modulus the value of x remains positive irrespective to the value of y.

Thus sufficient.

Option : B

Hemanth, good try! But [spoiler][/spoiler] is not the correct answer.

Lets modify the problem slightly to make two new problems.

Modification 1:
Is x non-negative?
(1) |x^2| = 3
(2) |6 - 5y| = x

Modification 2:
If y is an integer, is x positive?
(1) |x^2| = 3
(2) |6 - 5y| = x

If you solve these, you'd know why [spoiler][/spoiler] is not the correct answer to the original problem.

aneesh.kg.. I'm struck man.. My wild guess (which is the only option, i'll have if this prob appears during my actual GMAT) will be E..

Do explain me your answer.. And if possible some basics of the above function..

Hemanth.

The correct answer is C. Note that the question implying that x is positive means x must always be greater than 0.

Statement 1 is insufficient since x^2 = 3 => x = sqrt(3) or -sqrt(3)

Statement 2 is insufficient because note that since we're not told y has to be an integer, y can take on the value 6 - 5y = 0 => y = 6/5. If this was the case, then x = 0 (Not positive).

Combining both statements, we can see that x can only take on the value x = sqrt(3) since a modulus is always positive.

Statement 1:
x = (3)^0.3 or - (3)^0.5
INSUFFICIENT

Statement 2:
x = Modulus of something
Therefore x must be 0 or greater than zero
INSUFFICIENT

Combining the two, x = (3)^0.5, which is positive.

Therefore, [spoiler][C][/spoiler] is correct.