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07 Sep 2004, 19:58
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n is to be chosen from ints 1 thru 96
what is the p thatn n (n+1) (n+2) is div by 8
a. 1/4
b. 3/8
c. 1/2
d/ 5/8
e 3/4
what is the p thatn n (n+1) (n+2) is div by 8
a. 1/4
b. 3/8
c. 1/2
d/ 5/8
e 3/4
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07 Sep 2004, 20:52
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C) 1/2
As long as we have a mutiple of 8 in the answer, it is divisible by 8
n=2 --> 2*3*4 = 8*3 = ok
n=4 --> 4*5*6 = 8*15 = ok
n=6 --> 6*7*8 = 8*42 = ok
... you see the pattern
As long as we have a mutiple of 8 in the answer, it is divisible by 8
n=2 --> 2*3*4 = 8*3 = ok
n=4 --> 4*5*6 = 8*15 = ok
n=6 --> 6*7*8 = 8*42 = ok
... you see the pattern
07 Sep 2004, 20:54
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The answer is 5/8. D.
Here's how:
Total number of ways that you can have a product n(n+1)(n+2) out of the integers 1 thru 96 = 96.
If you have an even integer as n, then n+2 will also be an even integer. For all of these cases, with n as an even integer, the product is divisible by 8. This accounts for half the total possibilities: 48. Examples:
2,3,4 divisible; 4,5,6 divisible; 6,7,8 divisible; and so on.
For the cases where n is an odd integer, n+2 must also be an odd integer. Product of two odd integers is another odd integer, which is not divisible by 8. Our only redemption here will be the cases where we have a multiple of 8 as the middle integer (n+1). This can only happen 12 times between integers 1 and 96.
Thus, our total divisibility cases = 48 + 12 = 60
Required probability = 60/96 = 5/8.
PS. Nice question!
Here's how:
Total number of ways that you can have a product n(n+1)(n+2) out of the integers 1 thru 96 = 96.
If you have an even integer as n, then n+2 will also be an even integer. For all of these cases, with n as an even integer, the product is divisible by 8. This accounts for half the total possibilities: 48. Examples:
2,3,4 divisible; 4,5,6 divisible; 6,7,8 divisible; and so on.
For the cases where n is an odd integer, n+2 must also be an odd integer. Product of two odd integers is another odd integer, which is not divisible by 8. Our only redemption here will be the cases where we have a multiple of 8 as the middle integer (n+1). This can only happen 12 times between integers 1 and 96.
Thus, our total divisibility cases = 48 + 12 = 60
Required probability = 60/96 = 5/8.
PS. Nice question!
, but I have often seen usage of "that are" for people. Shouldn't it be "who are"?
