If n is an integer, how many values of n will give an integral value of $$\left( {\frac{{16{n^2} + 7n + 6}}{n}} \right)$$   ?

A. 2

B. 3

C. 4

D. None of these

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & = \left( {\frac{{16{n^2} + 7n + 6}}{n}} \right) \cr & = \left( {\frac{{16{n^2}}}{n} + \frac{{7n}}{n} + \frac{6}{n}} \right) \cr & = \left( {16n + 7 + \frac{6}{n}} \right) \cr} $$
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.