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A number is selected at random from the set of integers{

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A number is selected at random from the set of integers{ [#permalink] New post 25 Sep 2005, 08:20
A number is selected at random from the set of integers{ 1,2,3,... 1000}. What is the probability that it is divisible by 4 but neither by 5 nor by 7?
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 [#permalink] New post 25 Sep 2005, 08:47
33/200

there are 1000/4 = 250 numbers divisible by 4
there are 1000/(4*5) = 50 numbers divisible by both 4 & 5
there are 1000 / (4*7) = 35 numbers divisible by both 4 & 7
there are 100/lcm(35, 50) or 1000/350 = 7 numbers divisible by both 5 & 7
there are 1000/ lcm (4, 20, 35) or 1000/700 numbers divisible by all 4, 5 & 7

numbers divisible by 4 but not by 5 or 7 = 250 - (50 + 35) + 7 + 1 = 172

p = 172/1000 or 0.172

Last edited by duttsit on 25 Sep 2005, 10:41, edited 2 times in total.
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 [#permalink] New post 25 Sep 2005, 08:56
Is it 7/40?
I get the probability of getting a number divisible by 4 as 1/4 and the probability of getting a number divisible by 4 AND either 5 or 7 as 3/40. So, subtracting the latter from the former, I got the answer.

Last edited by anandsebastin on 25 Sep 2005, 09:01, edited 1 time in total.
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 [#permalink] New post 25 Sep 2005, 08:58
This one is from a textbook which only gives the OA, no explanation.

The OA is 0.172.
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 [#permalink] New post 25 Sep 2005, 11:44
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  [#permalink] 25 Sep 2005, 11:44
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A number is selected at random from the set of integers{

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