In this task, you need to provide the correct option for a given problem from the provided options.

[EX Q]: Problem: if p and q are both odd prime numbers andp < q , then how many different positive integer factors does 2 pqhave ? 
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
[EX A]: d

[EX Q]: Problem: there are 12 slate rocks , 16 pumice rocks , and 8 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ? 
Options: a ) 3 / 32 , b ) 7 / 64 , c ) 11 / 105 , d ) 15 / 127 , e ) 19 / 134
[EX A]: c

[EX Q]: Problem: in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 16 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ? 
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60
[EX A]:
e