If a gym class is divided into 4 equal teams, 2 students have to sit out; 5 teams, 1 student has to sit out; 6 teams, 4 students have to sit out. If there are fewer than 70 people in the class, what is the minimum number of students that need to be added so that the class can be divided into 4,5, and 6 equal teams with no students sitting out?

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Mathematics

28 October, 17:56

If a gym class is divided into 4 equal teams, 2 students have to sit out; 5 teams, 1 student has to sit out; 6 teams, 4 students have to sit out. If there are fewer than 70 people in the class, what is the minimum number of students that need to be added so that the class can be divided into 4,5, and 6 equal teams with no students sitting out?

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Steve Bates · Answer 1

x = number of students in the class

"there are fewer than 70 people in the class"

x < 70

x must be divisible by 4,5 and 6.

x must be a multiple of 5

x can't end with a 5, because it won't be divisible by 4 or 6. This means x must end with a 0.

List the multiples of 6 and 4 till you find their highest common factor.

x = 60