A hotel arranged cars to transport its guests to a venue

题目

A hotel arranged cars to transport its guests to a venue. If 4 guests were assigned to each car, the number of guests left over would be evenly divisible by both 6 and 9. When the hotel instead sent 5 guests in each car, the remaining guests had to take a taxi. If the total number of guests was between 40 and 60, what is the minimum number of guests who took a taxi?

选项

解析

某酒店安排车辆送客人前往场地。如果每辆车安排 4 位客人，则最后剩下的客人数能同时被 6 和 9 整除。若酒店改为每辆车坐 5 位客人，多余的客人需打车。已知总人数在 40 到 60 之间，问最少有多少人需要打车？每辆车坐 6 人，或是在减去 4 人后每辆车坐 9 人，那么剩余的人数必须同时能被 6 和 9 整除，也就是能被 6 和 9 的最小公倍数 18 整除。已知总人数在 40 到 60 之间，因此减去 4 人后的人数应为 54，总人数即为 58 人，每车5人，剩余3人；该题答案为 3。

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