Quote:
A hotel had 180 rooms numbered from 1 to 180. The rooms numbered from 25 to 180 were occupied and the rest were vacant. Two attendants, Kris and Michel, were given the duty of room service of occupied rooms. Each room numbered multiple of 3 was assigned to Kris and each room numbered multiple of 4 was given to Michel. If the rooms which were common for Kris and Michel, and rest of the unassigned occupied rooms were assigned to a third attendant named George, how many rooms were assigned to George?
A. 82
B. 91
C. 98
D. 99
E. 100
Rooms occupied = From number 25 to 180 = 156
Rooms vacant = 180 - 156 = 24
Each room numbered multiple of 3 was assigned to Kris
CONCEPT: Total rooms that are multiples of 3 from 1 to 180 = 180/3
Total rooms that are multiples of 3 from 1 to 24 = 24/3
i.e. Total rooms that are multiples of 3 from 25 to 180 = (180/3) - (24/3)i.e. Room Numbers assigned to Chris = (180/3) - (24/3) = 60 - 8 = 52 room
i.e. Room Numbers assigned to Michel = (180/4) - (24/4) = 45 - 6 = 39 room
Common rooms assigned to Chris and Michel = (180/12) - (24/12) = 15 - 2 = 13 rooms
Total Rooms assigned to Chris and Michel = 52+39 - (Common assignments) = 91 - 13 = 78
Rooms assigned to George = Unassigned occupied rooms + Common = (156 - 78) + 13 = 91 rooms
Answer: Option B