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Sets

by [email protected] » Tue Jul 22, 2008 6:00 am
Hi

Can someone help me understand how to answer this question please.

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

(1)For any integer in P, the sum of 3 and the integer are also in P

(2)For any integer in P , that integer minus 3 is also in P.

Thanks in advance
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by wilderness » Tue Jul 22, 2008 8:25 am
and is in P,
Is something missing in the question ?
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by [email protected] » Tue Jul 22, 2008 8:39 am
appologies it was meant to read

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 the integer are also in P

(2)For any integer in P , that integer minus 3 is also in P.
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by cubicle_bound_misfit » Tue Jul 22, 2008 9:28 am
Please let me know OA.
IMO it is E.

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by Canman » Tue Jul 22, 2008 9:44 am
I'm also going with E

Both statements, together or separately, do not appear to define P in any way such that we can conclude whether P contains all multiples of 3.
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by Ian Stewart » Tue Jul 22, 2008 10:36 am
[email protected] wrote:appologies it was meant to read

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 the integer are also in P

(2)For any integer in P , that integer minus 3 is also in P.
The answer should be A. We want to know if P contains all the positive multiples of 3- that is, we want to know if all of the numbers 3, 6, 9, 12, 15, etc... are in P. Assume 1) is true: if x is in P, then x+3 is in P. We know 3 is in P. So 3+3 = 6 is in P. And if 6 is in P, then 6+3 = 9 is in P. And so on- every positive multiple of 3 must be in P.

Statement 2) is not sufficient. We only know that 3 is in P. From 2), we know that 3-3 = 0 is in P, and thus that 0-3 = -3 is in P, and so on. From 2) we would know that every negative multiple of 3 is in P, but we don't know enough to conclude that any positive multiple of 3 is in P, with the exception of 3 itself.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by [email protected] » Tue Jul 22, 2008 11:31 am
Great thanks very much for your response Ian!
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by cubicle_bound_misfit » Tue Jul 22, 2008 10:01 pm
IAN

:idea:

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