PGMAT wrote:Set A consists of all the integers between 10 and 21, inclusive. Set B consists of all the integers between 10 and 50 inclusive. If x is a number chosen randomly from Set A, y is a number chosen randomly from set B, and y has no factor z such that 1 < z < y, what is the probability that the product xy is divisible by 3?

Note that from the definition y is nothing but a prime integer.

Set A has (21 - 10 + 1) = 12 integers
Set B has (50 - 10 + 1) = 41 integers

Hence, total number of possible values of xy = 12*41

Now, multiples of 3 in set A are: 12, 15, 18, and 21 --> 4 integers
And, prime numbers in set B are: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47 --> 11 integers

Hence, total number of possible values of xy such that xy is a multiple of 3 = 4*11

Hence, required probability = (4*11)/(12*41) = 11/(3*41) = 11/123

Note : The answer would have been B if set B had only the prime integers between 10 and 50.