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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
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If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 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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Kudos [?]: 77 [0], given: 3

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Re: DS: Sets [#permalink]

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New post 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.

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Re: DS: Sets [#permalink]

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New post 03 Jul 2009, 05:50
Thanks for the explanation..

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Senior Manager
Senior Manager
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Joined: 12 Mar 2006
Posts: 363

Kudos [?]: 77 [0], given: 3

Schools: Kellogg School of Management
Re: DS: Sets [#permalink]

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New post 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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Re: DS: Sets [#permalink]

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New post 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.

Kudos [?]: 29 [0], given: 4

Re: DS: Sets   [#permalink] 03 Jul 2009, 21:46
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If P is a set of integers and 3 is in P, is every positive

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