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

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Current Student
Joined: 31 Aug 2007
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If P is the set of integers and 3 is in P, is every positive [#permalink]  12 Dec 2007, 08:05
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Q. If P is the set of integers and 3 is in P, is every positive multiple of 3 in P?

a. For any integer in P, the sum of 3 and that integer is also in P.
b. For any integer in P, that integer minus 3 is also in P.
Director
Joined: 12 Jul 2007
Posts: 864
Followers: 13

Kudos [?]: 224 [0], given: 0

I'm getting D for this one.

1. If 3 is in P and the sum of 3 and any integer in P is also in P then...

3+3 = 6 +3 = 9 + 3 = 12, etc all have to be in P

you can also go the other way and say

x +3 = 3 has to be in there (so 0, -3, -6, -9, etc all count)

2. If 3 is in P and any integer -3 is also in P

3-3 = 0 -3 = -3 -3 = -6 etc

and again, you can go the other way and say

x-3 = 3 so x = 6 and (3, 6, 9, 12, etc all count)

so my answer is D here.
Manager
Joined: 01 Sep 2007
Posts: 101
Location: Astana
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Not sure but i think it is A because the question asks for a positive multiple of 3 and it does not follow from statement II.
Director
Joined: 12 Jul 2007
Posts: 864
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Kudos [?]: 224 [0], given: 0

CaspAreaGuy wrote:
Not sure but i think it is A because the question asks for a positive multiple of 3 and it does not follow from statement II.

yeah, upon further review I'm going to agree with A.

I thought you could say that 3 is in the set, and x-3 = 3 so that means 6 is in the set. However, I made the assumption that because a number X is in the set, X +3 had to be as well.
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