Concept: The question tests on equations in a DS format


Given x = u^2 – v^2 , y = 2uv and z = u^2 + v^2 . We also know x = 11, therefore, u^2 – v^2 = 11.

From statement I alone, y = 60.

 Therefore, 2uv = 60 or uv = 30. We can express u in terms of v as u = 30/v.

Substituting this in the equation u2 – v2 = 11 and solving the resulting quadratic equation, we obtain the value of v as 5.

Since uv = 30, we can now find the value of u and hence we can find the value of u^2 + v^2.

We don’t have to go beyond this stage and find the exact value of this expression since this is a DS question.

Statement I alone is sufficient. Answer options B, C and E can be eliminated. Possible answer options are A or D.

From statement II alone, u = 6.
 Therefore, u^2 = 36.

We also know that u^2 – v^2 = 11.

 Solving the two equations, we can find the value of v^2 and hence the value of z.

Statement II alone is sufficient. Answer option A can be eliminated.

 The correct answer option is D.