2001 AMC 10 Problems/Problem 8

Problem

Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how many school days from today will they next be together tutoring in the lab?

$\textbf{(A) }42\qquad\textbf{(B) }84\qquad\textbf{(C) }126\qquad\textbf{(D) }178\qquad\textbf{(E) }252$

Solution

We need to find the least common multiple of the three numbers given.

$\textrm{LCM}(15, 20, 25) = \textrm{LCM}(3 \cdot 5, 2^2 \cdot 5, 5^2) = 2^2 \cdot 3 \cdot 5^2 = 300$

300 minutes equals 5 hours. So the bell will ring 5 hours past 12:00, which is 17:00.

2001 AMC 10 (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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2001 AMC 10 Problems/Problem 8

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