For any integer
k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k . For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3 y < 1000, what is the maximum possible sum of the length of x and the length of y ?

5
6
15
16
18

How to solve this question within 2 mins? Trying out values for x and y is time consuming.