HMMT 十一月 2019 · 团队赛 · 第 1 题

HMMT November 2019 — Team Round — Problem 1

[20] Each person in Cambridge drinks a (possibly different) 12 ounce mixture of water and apple juice, where each drink has a positive amount of both liquids. Marc McGovern, the mayor of Cambridge, drinks 1 1 of the total amount of water drunk and of the total amount of apple juice drunk. How many people 6 8 are in Cambridge?

解析

[20] Each person in Cambridge drinks a (possibly different) 12 ounce mixture of water and apple juice, where each drink has a positive amount of both liquids. Marc McGovern, the mayor of Cambridge, drinks 1 1 of the total amount of water drunk and of the total amount of apple juice drunk. How many people 6 8 are in Cambridge? Proposed by: Alec Sun Answer: 7 The total amount of liquid drunk must be more than 6 times of the amount that Marc drinks but less than 8 times of the amount that Marc drinks. Therefore, the number of people in Cambridge is more than 6 but less than 8, so it must be 7.