A bomb squad consisting of three members, person C had to defuse the bomb while other members (A,B) had the task to detect the bomb. The bomb squad was summoned to the bank to defuse 2 bombs located inside the two of the 50 rooms of the bank.
The bank was divided into two sections, room number 1-25 were in section A and 26-50 were located in section B. For efficiency, person A went to the section A and person B went to the section B to detect the bomb. They detected the three possible rooms with the bomb and came back to report the room numbers to the person C. BUT, on the way back they forgot the room numbers of three rooms. However, person A knows that the multiplication of all three room numbers is 84, and person B knows that sum of all three room numbers is 92.
Person C knows that the sum of the room numbers in which the bomb is located is 53. Because of lack of time, Person C can only check 4 rooms of the whole bank (consider negligible time is taken during traversing the bank).
Can the person C defuse the bomb in time? If not, how many rooms do he need to check in order to defuse the bombs?