GWD4-9

[cmuboys]

Can someone tell me why the answer is D?

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

[clbb]

我的方法很慢...

(1)設n+1是偶數且為8的倍數:

(n+1)=8,16,24,....,96，n=7,15,23,....,95　　共有12個數　　　　　


(2)設n是偶數

　　(2).1：n是4的倍數:　　　 　　 　　　　　 n=4,8,12,.....,96　共24個

　　(2).2：n+2是4的倍數:(n+2)=4,8,...,96　n=2,6,10,....,94 　 共24個

所以機率為(12+24+24)/96=5/8