Question 72110: A group of people wanted to form committees each of which had the same number of persons; everyone in the group was to serve on a committee. When the group tried to make 2, 3, 4, 5, or 6 committees, there was always one extra person. However, they wer able to make more than 6 but fewer than 12 committees of equal size.
a. What was the smallest possible number of persons in the group?
b. How many persons were on each committee that was formed?
Answer by 303795(602)   (Show Source):
You can put this solution on YOUR website! The smallest number that 2, 3, 4, 5 and 6 all go into is 60. Therefore 61 will have a remainder of 1 for each of those numbers.
However none of 7, 8, 9, 10 and 11 are factors of 61 so the number cannot be 61.
The next smallest number that 2, 3, 4, 5 and 6 all go into with a remainder of 1 is 121. 11 is a factor of 121.
Therefore the smallest number of persons is 121. The number of committees formed is 11 each with 11 members.
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