Question 1204981
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If n is an integer between 1 and 96 (inclusive), what is the probability that n(n+1)(n+2) is divisible by 8?
a.1/4 b.1/2 c.5/8 d.3/4 e.7/8
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<pre>
Consider the REDUCED set of numbers  {1,2,3,4,5,6,7,8}.


Count, how many times n*(n+1)*(n+2) is divisible by 8 for n = 1,2,3,4,5,6,7,8


   T     A     B     L     E


n    n*(n+1)*(n+2)   divisibility
                        by 8
-------------------------------------
1         6

2        24             (*) 

3        60    

4       120             (*)

5       210

6       336             (*)

7       504             (*)

8       720             (*)


In the table, I marked all these cases (*) and got 5 cases of divisibility by 8.


This picture will repeat cyclically every 8 consecutive positive integer numbers.


So, the probability under the problem's question is  5/8.    <U>ANSWER</U>
</pre>

Solved.