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Data Sufficiency - Integers Question

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by jamie_700 » Tue Oct 27, 2009 9:10 am
Hi all, I've come across this data sufficiency question on integers and I have some serious trouble understanding its concept.

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.

Thank you in advance!
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Source: — Data Sufficiency |
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by crackgmat007 » Tue Oct 27, 2009 10:54 am
Is it A?

Question is asking whether every positive multiple of 3 is in Set P.

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

This statement confirms that all negative multiples of 3 are in set P.

Question states that 3 is in the set. THis means that 3-3 = 0, 0-3 = -3 & so on are in the set...

1) For any integer in P, the sum of 3 and that integer is also in P.

Using the same approach we can answer the question as yes.

HTH
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by mehravikas » Tue Oct 27, 2009 12:40 pm
IMO - E

Set could be - 0, 3, 6, 9 or 0, 1, 2, 3, 4, 5
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by crackgmat007 » Tue Oct 27, 2009 1:14 pm
mehravikas wrote:IMO - E

Set could be - 0, 3, 6, 9 or 0, 1, 2, 3, 4, 5
I guess we can still answer the question 'is every positive multiple of 3 in P?'

Can you let me know your reasoning?
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Re: Data Sufficiency - Integers Question

by Stuart@KaplanGMAT » Tue Oct 27, 2009 3:23 pm
jamie_700 wrote:Hi all, I've come across this data sufficiency question on integers and I have some serious trouble understanding its concept.

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.
Question: are {3, 6, 9, 12, ...} all in set P?

(1) if n is in P, then so is n + 3

Well, we know that 3 is in the set. Therefore, 3+3=6 is in the set. Therefore, 6+3=9 is in the set... and so on, and so on, and so on ... Are all the positive multiples of 3 in the set? Definitely YES: sufficient.

As Mehravikas notes, there could certainly be other numbers in the set as well. Do we care? Nope - the question doesn't ask "are ONLY all the positive multiples of 3 in the set?", so other numbers are irrelevant.

(2) if n is in P, then so is n - 3

The only number we know about for sure is 3, so all we know is that {3, 0, -3, -6, ...} are in the set. Is it possible that all positive multiples of 3 are there as well? Sure. Do they have to be there? No. Therefore, (2) is insufficient.

(1) is sufficient, (2) is insufficient: choose (A).

edit: bad use of question mark!
Last edited by Stuart@KaplanGMAT on Wed Oct 28, 2009 3:09 pm, edited 2 times in total.
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by mehravikas » Wed Oct 28, 2009 1:01 pm
My mistake...I misread the question.

We can still prove it by statement 1.

Thanks Stuart.
crackgmat007 wrote:
mehravikas wrote:IMO - E

Set could be - 0, 3, 6, 9 or 0, 1, 2, 3, 4, 5
I guess we can still answer the question 'is every positive multiple of 3 in P?'

Can you let me know your reasoning?
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by jamie_700 » Wed Oct 28, 2009 9:29 pm
Thanks for all the help on this question guys. In particular, thank you Stuart for the thorough explainations. Its all very helpful!
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