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

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Manager
Joined: 16 Apr 2009
Posts: 219
Schools: Ross
If P is a set of integers and 3 is in P, is every positive [#permalink]

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13 May 2009, 19:59
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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 and 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: 02 Mar 2009
Posts: 43
Location: Austin

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13 May 2009, 20:12
D

Each statement is sufficient to prove that "P" will not contain all positive multiples of 3.

ex. 4.5 is a multiple of 3 but will not be contained in "P",since "P" is restricted to a set of integers.
Director
Joined: 23 May 2008
Posts: 762

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13 May 2009, 22:02
E

both statements alone and together tell us only that there are multiples of 3 in the set. There is no way we can tell if EVERY multiple of 3 is in this set

(packem, 4.5 is not a multiple of 3......4.5/3 is not an integer)
Intern
Joined: 02 Mar 2009
Posts: 43
Location: Austin

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14 May 2009, 04:52
You're right.

Then, the answer should be A.

Statement I is sufficient to say that all positive integers of 3 are in P, since 3 is in "P" and every integer plus 3 is also in "P".
Manager
Joined: 11 Apr 2009
Posts: 157

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14 May 2009, 11:45

1. if you have 3 and 11 = 14 , which is not a multiple of 3 but can be a member of set P. On the other hand there is 18 which is a sum of 3 and 15 and is a multiple of 3.

2. The same logic applies to statement 2 also.

Let me know if anyone has any alternate explanation.
What is the OG btw?
Manager
Joined: 16 Apr 2009
Posts: 219
Schools: Ross

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17 May 2009, 09:54
Quote:
You're right.

Then, the answer should be A.

Statement I is sufficient to say that all positive integers of 3 are in P, since 3 is in "P" and every integer plus 3 is also in "P".

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Keep trying no matter how hard it seems, it will get easier.

Manager
Joined: 30 Mar 2009
Posts: 242

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24 May 2009, 03:12
IMO A

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 and that integer is also in P --> 3 in P, so 3 + 3 = 6 in P, 6 + 3 = 9 in P --> (all positive multiple of 3 in P)--> sufficient
2.For any integer in P,that integer minus 3 is also in P --> we only know that 3 in P, but not any other number. Therefore, we only prove that 3 - 3 = 0 in P, 0 - 3 = -3 in P ... (all negative, but not any positive mutiple of 3) --> not sufficient
Re: Multiple   [#permalink] 24 May 2009, 03:12
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