If x is a positive integer such that 2x + 12 is perfectly divisible by x then the number of possible values of x is

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Solution

The correct option is C 6
If (2x + 12) is perfectly divisible by x, then (2x + 12)/x has to be an
integer as x is an integer. Now if we divide, the expression simplifies
to (2 + 12/x). The only way in which this expression would be an integer
is when 12/x is an integer or if 12 is perfectly divisible by x. This
is possible if x takes either of these values : 1, 2, 3, 4, 6, 12. Hence
the answer is 6 values.

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