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# Stumped on this Data Sufficiency question...

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Stumped on this Data Sufficiency question... [#permalink]  10 Apr 2008, 10:09
This question came from math bin 3 in the Princeton Review 2008 book.

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.

My reasoning is that each statement alone is sufficient, because...

stmt. 1 - any positive multiple of 3 is included because it could be 0 + 3 = 3, 3 + 3 = 6...., 9 + 3 = 12, etc.

stmt. 2- this could be 3 - 3 = 0, 6 - 3 = 3, and so on. so all positive multiples of 3 should also be included right?

According to the PR explanations, statement 2 gives all the negative multiples of 3 and that the correct answer is:
statement 1 alone is sufficient, but statement 2 alone is not sufficient.

Is this an error in the book or am I completely overlooking something?
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Re: Stumped on this Data Sufficiency question... [#permalink]  10 Apr 2008, 12:28
As per question If P is a set of integers and 3 is in P. Let us assume that to start with P contains only 3.

Statement 1:
Tells us that for any integer in P, the sum of 3 and that integer is also in P. As we already have 3 as part of P, so what follows is we have 3+3 = 6, 6+3 =9, 9+3 = 12...... etc. as part of P. So question is answered.

Statement 2:
Tells us for any integer in P, that integer minus 3 is also in P. As we already have 3 as part of P, so what follows is we have 3-3 = 0, 0-3 = -3, -3-3 = -6,....etc. as part of P. So question is not answered.

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Re: Stumped on this Data Sufficiency question... [#permalink]  10 Apr 2008, 13:37
ty. that makes much better sense now.
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Re: Stumped on this Data Sufficiency question... [#permalink]  10 Apr 2008, 15:25
For any integer in P, the sum of 3 and that integer is also in P.

why are you not considering numbers 1,2,4,5 in Stmt-1
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Re: Stumped on this Data Sufficiency question... [#permalink]  10 Apr 2008, 18:46
prasannar wrote:
For any integer in P, the sum of 3 and that integer is also in P.

why are you not considering numbers 1,2,4,5 in Stmt-1

I get it now... the question only confirms that the number 3 is in the set. so only 3, 3+3 or 6, 6+3 or 9, 9+3 or 12, etc. are in this set according to statement 1.
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Re: Stumped on this Data Sufficiency question... [#permalink]  10 Apr 2008, 18:54
prasannar wrote:
why are you not considering numbers 1,2,4,5 in Stmt-1
For any integer in P, the sum of 3 and that integer is also in P.

why are you not considering numbers 1,2,4,5 in Stmt-1

Argree with prasannar,
No clues say that you must start from 3+3! Why not from 3+2?
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Re: Stumped on this Data Sufficiency question... [#permalink]  11 Apr 2008, 04:31
prasannar wrote:
For any integer in P, the sum of 3 and that integer is also in P.

why are you not considering numbers 1,2,4,5 in Stmt-1

Question is asking abouy whether all the +ve multiples of 3 is present in series or not. Which we can answer from the information present in the question. Even if 1,2 etc. are there that would not add much value in answering the question.
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Re: Stumped on this Data Sufficiency question... [#permalink]  11 Apr 2008, 07:59
With the same logic, statement 2 can be proved as well. Not sure why the answer is A .
The multiples of 3 may or may not be present in either of the statements.

Ama have to go with E here folks .

Explanation anyone ?
Re: Stumped on this Data Sufficiency question...   [#permalink] 11 Apr 2008, 07:59
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