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

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If P is a set of integers and 3 is in P , is every positive [#permalink]  19 Aug 2007, 16:59
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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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Re: DS Problem I don't understand [#permalink]  19 Aug 2007, 17:06
troy3626 wrote:
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.

A.

The question is asking if P = {3, 6, 9, 12, ... , infinite multiple of 3)

(1) If 3 is in P, then 3+3 is in p, 3+3+3 is in P, 3+3+3+3 is in P; thus, SUFFICIENT.

(2) Can't conclude from this, since we only know that 3 is in P. Same logic as above, but we can only conclude that all negative multiples are in P, but not positive multiples.
INSUFFICIENT.
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St1:
Sufficient. We're told 3 is in set P, and 3+any integer must also be in P. so 3+3 must be in P, an so must 3+6, 3+9 etc... so all multiples of 3 are in P.

St2:
Insufficient. If our set is P={3,6,9,12}, then 12-3 = 9 must be in the set, 9-3 = 6 must be in the set, but this set doesnt' contain all the multilpes of 3.

Ans A
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Re: DS Problem I don't understand [#permalink]  19 Aug 2007, 19:43
troy3626 wrote:
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.

hmmm i get E for the answer

for (1) how do we not know that 0 is not part of the set. P is just a set of integers, we don't know if they are negative, positive, or 0. It still holds true for 0 + 3 = 3. In that case, 0 wouldn't be a positive multiple of 3 right?
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Re: DS Problem I don't understand [#permalink]  19 Aug 2007, 20:48
beckee529 wrote:
troy3626 wrote:
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.

hmmm i get E for the answer

for (1) how do we not know that 0 is not part of the set. P is just a set of integers, we don't know if they are negative, positive, or 0. It still holds true for 0 + 3 = 3. In that case, 0 wouldn't be a positive multiple of 3 right?

A. it doesnot say only +ve. if 0 is in p, then 3 is there and all other +ve multiple of 3 too.
so Suff.
Re: DS Problem I don't understand   [#permalink] 19 Aug 2007, 20:48
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