AP ICET 2015 Paper

Given: x and y are real numbers.
I. Given: $\mathit{x}+\mathit{y}=16$
There are two unknowns and only one equation. Further, x and y being real numbers, we can have infinite number of solutions.
∴ Ι alone is not sufficient
II. Given: ${\mathit{x}}^2+{\mathit{y}}^2=160$
Similarly, II alone is not sufficient.
I&II. $\mathit{x}+\mathit{y}=16,{\mathit{x}}^2+{\mathit{y}}^2=160$
${\left(\mathit{x}+\mathit{y}\right)}^2={\mathit{x}}^2+{\mathit{y}}^2+2\mathit{x}\mathit{y}$.
So we can find xy.
∴ I&II together are sufficient.