CAT 1997 — QA Question 11

The given expression can be written as

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

Since n is an integer, the expression (16n + 7) will always be an integer. Hence, for the entire expression to be an integer, the part $\left(\frac{6}{n}\right)$ should also be an integer.
This can be possible only if n is a factor of 6, viz. n = 1, 2, 3, 6, –1, –2, –3 and –6.

Hence, n can have eight values.