document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204981>Question 1204981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If n is an integer between 1 and 96 (inclusive), what is the probability that n(n+1)(n+2) is divisible by 8? <BR>\n" );
document.write( "a.1/4 b.1/2 c.5/8 d.3/4 e.7/8 </SPAN>\n" );
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document.write( "If n is even, then n+2 is even, and one of them (exactly one of them) is a multiple of 4.  So together the first and last of the three consecutive integers have 3 factors of 2, which makes the product divisible by 8.<br><BR>\n" );
document.write( "Half of the numbers 1 through 96 are even, so the probability is 1/2 that n is even and the product is divisible by 8.<br><BR>\n" );
document.write( "If n is odd, then n+2 is odd; for the product of the three consecutive integers to be divisible by 8, the middle number has to be divisible by 8.  Since 1 out of every 8 integers from 1 to 96 is divisible by 8, the probability is 1/8 that n is odd and the product is divisible by 8.<br><BR>\n" );
document.write( "The two cases of n even and n odd cover all possibilities, so the probability that the product is divisible by 8 is<br><BR>\n" );
document.write( "ANSWER: 1/2 + 1/8 = 5/8<br><BR>\n" );
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