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If P is a set of integers and 3 is in P, is every positive

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Senior Manager
Joined: 12 Mar 2006
Posts: 358
Schools: Kellogg School of Management
If P is a set of integers and 3 is in P, is every positive [#permalink]

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02 Jul 2009, 20:33
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If P is a set of integers and 3 is in P, is every positive multiple of 3 in P ?

(1) For any integer in P, the sum of 3 & that integer is also in P
(2) For any integer in P, that integer minus 3 is also in P

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Intern
Joined: 30 Jun 2009
Posts: 4

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02 Jul 2009, 22:03
from...statement1:
if one number is 3 then the other can be 3+3=6,the next can be 6+3=9,..and so on.all these number which you obtain above 3,6,9,12....so on are positive integral multiple of 3....hence sufficient....ok

from statement 2:
if one number is 3 the other can be 3-3=0,then next can be 0-3=-3,again
-3-3=-6....and so on....BUT here the number 0,-3,-6.....and so on are not positive integral multiple of 3.......(though there may be many numbers in p like 6-3=3,9-3=6,12-3=9 ...so on which may satisfy the condition)
...hence not sufficient.
Intern
Joined: 05 Sep 2006
Posts: 14

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03 Jul 2009, 05:50
Thanks for the explanation..
Senior Manager
Joined: 12 Mar 2006
Posts: 358
Schools: Kellogg School of Management

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03 Jul 2009, 07:13
For statement 2 ... can we also use some kinda reverse logic to say since if number a is there a-3 is present in the set which means if a-3 is present in the set a is present as well ... but I guess that is wrong ....

thank you
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Manager
Joined: 28 Jan 2004
Posts: 199
Location: India

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03 Jul 2009, 21:46
What is the source of this queston and that is the OA ?

We can have set P as {1,3,4,6.........}
Ofcorse every multiple of 3 will be there as per stmt 1. but thats very obvious I guess if there is some trick to this question.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: DS: Sets   [#permalink] 03 Jul 2009, 21:46
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