bastencools 当前离线
金牌会员
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
A.1/4
B.3/8
C.1/2
D.5/8
E.3/4 答案是D,为什么呢?
strawdog 当前离线
中级会员
when n is an even integer, n(n+1)(n+2) will definitely be divisible by 8, there are 48 even numbers in total.
when n is an odd integer, n(n+1)(n+2) will only be divisible by 8 when (n+1) is divisible by 8, there are 12 numbers in total.
(48+12)/96=5/8
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bioliwu 当前离线
高级会员
1-96 INCLUSIVE
1) 连续数性质, 三个连续数相乘,中间为奇数,能被8 除.
这就有48个.从2*3*4---96*97*98
2)连续数中间为偶数8,或8的倍数.
7*8*9, 中间还有16,24,32,40,48,56,8K, 到,95*96*97,
共 12个
1)+2)为 60个.
一共有96个.
所以为 60/96=5/8
SunnyApples 当前离线
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