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What is the total number of integers between 100 and 200 that are divisible by 3
What is the total number of integers between 100 and 200 that are divisible by 3
游客
2024-01-12
40
管理
问题
What is the total number of integers between 100 and 200 that are divisible by 3?
选项
A、33
B、32
C、31
D、30
E、29
答案
A
解析
对于区间[a,b]中有多少个数能够被数n整除,计算方法如下:
第一步:把b往小里凑。找到最近的n的倍数,记为r;
比如例题中6为200,那么往小里凑,找到最近的3的倍数为198。
第二步:把a往大里凑,找到最近的n的倍数。记为s;
比如例题中a为100,那么往大里凑,找到最近的3的倍数为102。
第三步:区间[a,b]中有能够被数n整除的个数即为(r-s)/n+1。
比如例题中能够被3整除的个数为:(198-102)/3+1=33。
正确答案为A。
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