Question

If x is a positive integer such that 2x+12 is perfectly divisible by x, then the number of possible values of x is
a) 2
b) 5
c)6
d)12​

Answer 1

Answer:

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.