7) How many positive numbers $n$ are there such that $n+30>n^{2}$ ?

$\begin{array}{llll}\text { (A) infinite } & \text { (B) } 30 & \text { (C) } 6 & \text { (D) } 5\end{array}$

(E) none of the above answers is correct.
7) The answer is (D)

If we consider the expression $n^{2}-n-30$, we can easily see that it is increasing with the increase of $n$ if $n$ is positive (indeed $\left.\left[(n+1)^{2}-(n+1)-30\right]-\left[n^{2}-n-30\right]=2 n\right)$. Since for $n=6$ we have $n+30=36=n^{2}$, the numbers that satisfy the required condition are those less (strictly) than 6.