If n is an integer, how many values of n will give an integral value of ( 16n^2 + 7n + 6n ) ?

Answer: Option C

$$\begin{array}{rl}& =\left(\frac{16n^2+7n+6}{n}\right)\\ & =\left(\frac{16n^2}{n}+\frac{7n}{n}+\frac{6}{n}\right)\\ & =\left(16n+7+\frac{6}{n}\right)\end{array}$$
For $$\left(16n+7+\frac{6}{n}\right)$$   to be an integer, we may have n = 1 or n = 2 or n = 3 or n = 6
Hence, 4 value of n will give the desired result.