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N is between 1 and 99, inclusive. What’s the possibility of N( N+1) being the mu
N is between 1 and 99, inclusive. What’s the possibility of N( N+1) being the mu
游客
2024-01-13
34
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问题
N is between 1 and 99, inclusive. What’s the possibility of N( N+1) being the multiples of 3?
选项
A、65/9
B、64/99
C、1/3
D、2/3
E、1
答案
D
解析
正如正奇数偶数分别可以表示为2k+1,2k+2,其中k是整数一样,所有整数也可以表示为:3k+1,3k+2,3k+3,其中七是整数,对于乘积N(N+1)来说:
N=3k+1时,N(N+1)=(3k+1)(3k+2)不能够被3整除,
N=3k+2时,(3k+2)(3k+3)能够被3整除,
N=3k+3时,(3k+3)(3k+4)能够被3整除。
N从1到99,这99个数中能够表示为N=3k+2的数不能够被3整除,一共有33个,那么能够被整除的数有66个,所求概率为66/99=2/3。
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