capegemini - find the probability that a number selected at random from the set of two digit numbers will not be a multiple of 12 and not a multiple of 4 - skillgun

The two digit numbers are 10,11,12,...,99
There are 90 two digit numbers.
Since the set of multiples of 4 contains multiple of 12 then it's enough to find the number of multiples of 4.
The first two digit number that is divisible by 4 is 12 and every 4th number from 13 is multiple of 4.
Here, 22 (integral value of 90/4) numbers of multiples of 4 & 12 together.
Then the number of two-digit non-multiple of 12 and non-multiple of 4 is 90-22 = 68.
Hence the required ratio is 68/90 = 34/45.