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How many integers between 100 and 150, inclusive, can be evenly divided by neith
How many integers between 100 and 150, inclusive, can be evenly divided by neith
游客
2024-01-13
37
管理
问题
How many integers between 100 and 150, inclusive, can be evenly divided by neither 3 nor 5?
选项
A、33
B、26
C、24
D、28
E、27
答案
E
解析
此题考查整除和集合,evenly divided by 3其实就是被3整除的意思。从100到150被3整除的数的个数,我们在前面知识点中讲过有一个公式可以求
(150-102)/3+1=17。
同理,从100到150被5整除的数的个数为:
(150-100)/5+1=11。
但是我们要考虑到能够同时被3和5整除的数,也就是被15整除的数的个数:
在100到150内能够被3或者被5整除的数的个数是:17+11-4=24。
注意还有一个陷阱,在求既不能被3也不能被5整除的数的个数时,许多考生犯了一个错误,认为从100到150之间只有50个数,于是得到50-24=26,其实应该是一共有51个数,这样51-24=27。
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