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# For a set of numbers composed of positive integers ranging

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CEO
Joined: 15 Aug 2003
Posts: 3469
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Kudos [?]: 702 [0], given: 781

For a set of numbers composed of positive integers ranging [#permalink]  12 Sep 2003, 03:28
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For a set of numbers composed of positive integers ranging from 1-99
(inclusive),we take a number N from the set, what is the probability that
n*(n+1) is divisible by 3?
Senior Manager
Joined: 21 Aug 2003
Posts: 258
Location: Bangalore
Followers: 1

Kudos [?]: 4 [0], given: 0

Total ways to choose N = 99
Number of ways to choose N such that n*(n+1) is divisible by 3 = 33 + 33 = 66
{N must be a mutiple of 3 or one integer less than the multiple of 3 for above to hold true}
Thus, probability = 66/99 = 2/3
- Vicks
Manager
Joined: 02 Jul 2003
Posts: 58
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Kudos [?]: 0 [0], given: 0

Question for you Vicky. Is this correct- A quick way to find the multiples of three between 1 and 99 is to make 1=3^1 and 99=3*33. Thus the number of integers that are multiples of 3 is the number of integers between 1 and 33. Which would be 33.

Thanks,

Rich
Senior Manager
Joined: 21 Aug 2003
Posts: 258
Location: Bangalore
Followers: 1

Kudos [?]: 4 [0], given: 0

absolutely... smarter way to number of mutiples...
- Vicks
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