An organization has employee count < 5000. The organization wishes to conduct an annual sports meet. If the employees are divided equally into groups [9/10/12/25] it was found that 4 employees were left out. But, it was noticed that when groups of 11 each was formed, no one is left out. The maximum number of groups of 12 each that can be formed out of the players in the organization is
Question
An organization has employee count < 5000. The organization wishes to conduct an annual sports meet. If the employees are divided equally into groups [9/10/12/25] it was found that 4 employees were left out. But, it was noticed that when groups of 11 each was formed, no one is left out. The maximum number of groups of 12 each that can be formed out of the players in the organization is
Solution
The problem is asking for the number of employees in the organization that is divisible by 11 but leaves a remainder of 4 when divided by 9, 10, 12, and 25. This is a problem of finding the least common multiple (LCM) and then adding the remainder.
Step 1: Find the LCM of 9, 10, 12, and 25. The LCM of these numbers is 900.
Step 2: Find a number that when divided by 900 leaves a remainder of 4. This number is 904.
Step 3: Check if 904 is divisible by 11. It is not. So, we need to find the next number that is divisible by 900 and leaves a remainder of 4. This is done by adding 900 to 904 to get 1804.
Step 4: Check if 1804 is divisible by 11. It is not. Repeat step 3 and 4 until we find a number that is divisible by 11.
Step 5: After repeating the steps, we find that the number 3604 is divisible by 11 and when divided by 900 leaves a remainder of 4.
Step 6: Now, we need to find the maximum number of groups of 12 that can be formed from 3604 employees. This is done by dividing 3604 by 12. The answer is 300.
So, the maximum number of groups of 12 each that can be formed out of the players in the organization is 300.
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