There are 50 doors marked with numbers 1 to 50.
There are 50 doors marked with numbers 1 to 50. And there are 50 individuals marked 1 to 50.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with.
Now one at a time one randomly picked individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For e.g. individual marked with number 5 operates the doors marked with the following numbers: 5, 10, 15 ... 50.
If every individual in the group get one turn then how many doors are open at the end?
Answer/Solution
7
Steps/Work
Let us start with 1.
When 1 goes, all the doors are open since every number is a multiple of 1.
Also 1 will remain opened since 1 is not a multiple of any number.
Prime numbers can only be operated by people with prime numbers.
So 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 will be closed when people with respective numbers perform operations on them.
From the other numbers, only those numbers will remain opened on which even number of operations are performed including the operation performed by number 1.
This is possible only for perfect squares which are 4,9, 16,25,36 and 49.
So our numbers are 1,4,9,16,25,36 and 49.
Answer:- E
When 1 goes, all the doors are open since every number is a multiple of 1.
Also 1 will remain opened since 1 is not a multiple of any number.
Prime numbers can only be operated by people with prime numbers.
So 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 will be closed when people with respective numbers perform operations on them.
From the other numbers, only those numbers will remain opened on which even number of operations are performed including the operation performed by number 1.
This is possible only for perfect squares which are 4,9, 16,25,36 and 49.
So our numbers are 1,4,9,16,25,36 and 49.
Answer:- E