$$Statement\ 1\ =\ a^2b\ >\ 0$$
Given that b is positive, a can be any number either positive or negative.
If a = -3 and b = 2 , then ab = -6 (negative)
If a = 3 and b =2 then ab = 6 (positive)
We do not have enough information to ascertain a definite answer, hence statement 1 is INSUFFICIENT.

$$Statement\ 2=\ a^2\ +\ b\ >\ 13$$
Given that b is positive, a can be either positive or negative.
$$If\ a\ =\ -3\ and\ \ b\ =\ 5;\ a^2\ +\ b\ =\ 13\ =\ -3^2\ +\ 5\ =\ 13$$
But, ab = -3 * 5 = -15 (negative)
$$If\ a\ =\ 3\ and\ \ b\ =\ 5;\ a^2\ +\ b\ =\ 13\ =\ 3^2\ +\ 5\ =\ 13$$
But, ab = 3 * 5 = 15 (positive)
Combining statement 1 and 2 together;
None of the statement provided specific information about the unknown variable 'a' ,
thus a can still be either positive or negative, this will also make ab to be either positive oe negative.
Hence, the two statement combined together are INSUFFICIENT.
Option E is correct.

BTGmoderatorDC wrote:If b is positive, is ab positive?

$$\left(1\right)\ a^2b\ >0$$
$$\left(2\right)\ a^2\ +\ b\ =\ 13$$

\[b > 0\]
\[ab\,\,\mathop > \limits^? \,\,0\]
\[\left( {1 + 2} \right)\,\,\left\{ \begin{gathered}
\,Take\,\,\,\left( {a,b} \right) = \left( {1,12} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\,Take\,\,\,\left( {a,b} \right) = \left( { - 1,12} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\
\end{gathered} \right.\]

The above follows the notations and rationale taught in the GMATH method.