There are 1000 doors that are of the open-close type. When a person opens the door he closes it and then opens the other. When the first person goes he opens-closes the doors in the multiples of 1 i.e., he opens and closes all the doors. when the second goes he opens and closes the doors 2, 4 6 8 respectively. Similarly when the third one goes he does this for 3 6 9 12 15th doors respectively. Find number of doors that are open at last.
Options:
(A) 29
(B) 31
(C) 32
(D) 24
(E) 21 OK. Let's think. Some random thoughts first:
31. only the perfect squares between 1 to 1k The answer: (B).