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

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New post 24 Jul 2011, 02:36
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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
[Reveal] Spoiler: OA

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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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New post 24 Jul 2011, 03:01
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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New post 27 Nov 2017, 03:06
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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.

Answer: A.


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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, 03:06
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