A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the students in the school is
Explanation:
The number of students will be of the form = LCM(9, 10, 12, 25) × k + 4 = 900k + 4
The number of students is less than 5000 and also completely divisible by 11. This is possible when k = 2 and hence the number the students = 1804.
Maximum number of groups of 12 students that can be formed = Quotient of [1804 / 12] = 150
Hence, 150.
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