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# If an integer n is chosen from the integers 1

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If an integer n is chosen from the integers 1 [#permalink]  28 Nov 2019, 00:04
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Question Stats:

40% (02:25) correct 60% (01:44) wrong based on 10 sessions
If an integer n is chosen from the integers 1 through 72,what is the probability that n*(n+1)*(n+2)will be divisible by 8

(a)1/4
(b)3/8
(c)1/2
(d)5/8
(e)3/4
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Re: If an integer n is chosen from the integers 1 [#permalink]  28 Nov 2019, 00:10
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n is Even
Since n is divisible by 2 then either one of n or n+2 will be divisible by 4. Hence the product ?(?+1)(?+2)will be divisible by 8. Total choices 36.

n is Odd
Then n and n+2 will both be odd and the only way this expression is divisible by 8 is when n+1 is divisible by 8. There are 72/8 such choices : (7,15,23,..,71).

So, combining 1 and 2 we have 36 + 9 = 45 choices for n. Which results in a probability of 45/72=5/8

This is not a GRE. You are doing the wrong practice
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Re: If an integer n is chosen from the integers 1 [#permalink]  06 Dec 2019, 03:38
Carcass wrote:
n is Even
Since n is divisible by 2 then either one of n or n+2 will be divisible by 4. Hence the product ?(?+1)(?+2)will be divisible by 8. Total choices 36.

n is Odd
Then n and n+2 will both be odd and the only way this expression is divisible by 8 is when n+1 is divisible by 8. There are 72/8 such choices : (7,15,23,..,71).

So, combining 1 and 2 we have 36 + 9 = 45 choices for n. Which results in a probability of 45/72=5/8

This is not a GRE. You are doing the wrong practice

(7,15,23,..,71) This case has already been counted as n being even(70). So the total cases are 44

It's a GRE question. I have the same username on GMAT club, so won't post a GMAT question here.
Re: If an integer n is chosen from the integers 1   [#permalink] 06 Dec 2019, 03:38
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