HMMT 二月 2002 · 代数 · 第 4 题
HMMT February 2002 — Algebra — Problem 4
题目详情
英文原题
- If a positive integer multiple of 864 is picked randomly, with each multiple having the same probability of being picked, what is the probability that it is divisible by 1944?
2 3
解析
英文解析
- If a positive integer multiple of 864 is picked randomly, with each multiple having the same probability of being picked, what is the probability that it is divisible by 1944?
5 3 3 5
Solution: The probability that a multiple of 864 = 2 3 is divisible by 2744 = 2 3 is
2 2
the same as the probability that a multiple of 2 is divisible by 3 , which since 4 and 9 arerelatively prime is .1
2 39