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imc

number theory intermediate

Problem

A single bench section at a school event can hold either adults or children. When bench sections are connected end to end, an equal number of adults and children seated together will occupy all the bench space. What is the least possible positive integer value of
(A)
(B)
(C)
(D)
Solution
The least common multiple of and is . Therefore, there must be adults and children. The total number of benches is .~taarunganesh
Final answer
B