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

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Manager
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Joined: 05 Jun 2011
Posts: 110
Location: Shanghai China
If P is a set of integers and 3 is in P, is every positive multiple of [#permalink]

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24 Jul 2011, 03:36
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Difficulty:

55% (hard)

Question Stats:

53% (01:05) correct 47% (01:07) wrong based on 38 sessions

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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-p-is-a-se ... 96630.html
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Joined: 03 Mar 2010
Posts: 400
Schools: Simon '16 (M)
Re: If P is a set of integers and 3 is in P, is every positive multiple of [#permalink]

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24 Jul 2011, 04:01
tracyyahoo wrote:
does it mean that 3 is x or x is 3?~

It means x(3) is in p.

Stmt1: if x is in p, then x+3 is in p
since 3 is in p, 3+3=6 is in p, 6+3=9 is in p, 9+3=12 is in p. Every positive multiple of 3 is in P

Sufficient.

Stmt2:if x is in p, then x-3 is in p
If x is 12, p={....0,3,6,9,12}
If x is 9, p={....0,3,6,9}
Clearly elements in set p depends upon value of x. Insufficient.

OA A.
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Re: If P is a set of integers and 3 is in P, is every positive multiple of [#permalink]

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27 Nov 2017, 04:06
If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

Positive multiples of 3 are: 3, 6, 9, 12, 15, ... The question asks whether ALL these numbers are in the set P, taking into account that 3 is in this set.

(1) For any integer in P, the sum of 3 and that integer is also in P --> if $$x$$ is in the set, so is $$x+3$$ --> we know 3 is in P, hence $$3+3=6$$ is also in, and as 6 is in so is $$6+3=9$$, and so on. Which means that ALL positive multiples of 3 are in the set P. Sufficient.

Side note: above does not mean that only positive multiples of 3 are in P, there can be other numbers but we are only interested in them.

(2) For any integer in P, that integer minus 3 is also in P --> if $$x$$ is in the set, so is $$x-3$$ --> we know 3 is in P, hence $$3-3=0$$ is also in and as 0 is in, so is $$0-3=-3$$, and so on. So we are not sure whether all positive multiples of 3 are in P, all we know that there will be following numbers: 3, 0, -3, -6, -9, -12, ... Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-p-is-a-se ... 96630.html
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Re: If P is a set of integers and 3 is in P, is every positive multiple of   [#permalink] 27 Nov 2017, 04:06
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