If x is a positive integer such that 2x + 12 is perfectly divisible by x, then the number of possible values of x is :
2
5
6
12
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2014
(2x + 12) / x = (2x / x) + (12 / x) = 2 + 12/x.
Since 2 is an integer, for the entire expression (2 + 12/x) to be an integer, 12/x must be an integer.
This means x must be a divisor of 12.
Since x is a positive integer, we need to find all positive divisors of 12.
The positive divisors of 12 are the numbers that divide 12 without leaving a remainder: 1, 2, 3, 4, 6, and 12.
There are 6 such positive integers.
If x=1, 2(1)+12 = 14, 14/1 = 14 (integer)
If x=2, 2(2)+12 = 16, 16/2 = 8 (integer)
If x=3, 2(3)+12 = 18, 18/3 = 6 (integer)
If x=4, 2(4)+12 = 20, 20/4 = 5 (integer)
If x=6, 2(6)+12 = 24, 24/6 = 4 (integer)
If x=12, 2(12)+12 = 36, 36/12 = 3 (integer)
All 6 values are valid.