If n is an integer, how many values of n will give an integral value of $\frac{(16 n^{z} + 7 n + 6)}{n} ?$ (CAT 1997)

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Solution

The correct option is C 4
Ans: (c)

$\frac{(16 n^{z} + 7 n + 6)}{n} = 16 n + 7 + \frac{6}{n};$
Since n is an integer, hence for the entire expression to become an integer, $(\frac{6}{n})$ should be an integer. And $(\frac{6}{n})$ can be integer for $n = 1, 2, 3, 6.$ Hence n has 4 values.

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