Problem:
On June , a group of students is standing in rows, with students in each row. On June , the same group is standing with all of the students in one long row. On June , the same group is standing with just one student in each row. On June , the same group is standing with students in each row. This process continues through June with a different number of students per row each day. However, on June , they cannot find a new way of organizing the students. What is the smallest possible number of students in the group?
Answer Choices:
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B.
C.
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E.
Solution:
The number of students must be a multiple of and also a multiple of . So the number of students must be divisible by the least common multiple of and which is . The divisors of are and , so there are only divisors. The divisors of are and . So has divisors and is the smallest possible number of students.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions