2010/11 AHSMC Part 1 Problem 6

Problem 6 of 16

Alice, Brian, Colin, Debra and Ethel are in a hotel. Their rooms are on floors $1$ , $2$ , $3$ , $21$ and $40$ respectively. In order to minimize the total number of floors they have to cover to get together, the floor on which the get-together should be is

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Solution

Alice and Ethel are $39$ floors apart, and as long as the get-together floor is in between, the total number of floors they cover is $39$ . Similarly, the total number of floors Brian and Debra cover is $19$ . The minimum number of floors Colin covers is $0$ , when they get together on floor $3$ . The answer is (E).

University of Alberta

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