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Integral Values of expression for values of n – CAT 1997 Question

Q.)If n is an integer , how many values of n will give an integral value of \frac { (16{ n }^{ 2 }+7n+6) }{ n } ?
(a)2
(b)3
(c)4
(d) None of these
[CAT 1997 Question,CAT Question,Number System]
Solution :

The expression \frac { (16{ n }^{ 2 }+7n+6) }{ n } can be rewritten as

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

The expression \frac { (16{ n }^{ 2 }+7n+6) }{ n } would be an integer only if \frac {6}{ n } also is an integer i.e. n should divide 6 without any remainder.

6 will be divisible by following integral values : 1,2,3,6,-1,-2,-3,-6

so, total possible values of n = 8

So, the number of values of n which would give integral value of \frac { (16{ n }^{ 2 }+7n+6) }{ n } = 8

Hence, OPTION(d)


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