If x is a positive integer such that 2x + 12 is perfectly divisible by x, then the number of possible values of x is
Explanation:
If (2x + 12) is perfectly divisible by x, then (2x + 12)/x has to be 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. [i.e., x is a factor of 12]
This is possible if x takes either of these values : 1, 2, 3, 4, 6, 12. Hence the answer is 6 values.
Hence, option (c).
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