In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number Q of employees who take the subway to work? Choose the correct choice from the following answers:  A) 12  B) 13  C) 14  D) 15  E) 16

Rationale: "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible q : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer"
Answer: D