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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]  01 Oct 2003, 15:43
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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.
Intern
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stolyar, shouldnt it be E.?

For any integer in the set,where 3 is a member of the set,the sum of 3 and that integer is in p.

lets say the number in the set is 5. then statement 1 says 5 and 8 are in the set.Why do we assume that all the members in the set r multiples of 3 like '3'.its given that 3 is a member of the set.it doesnt say that all the numbers in the set are multiples of 3.

just curious???
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I agree with Stolyar. The answer should be D

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

It is already given in the question stem that 3 is in the set P. So this statement sets the trigger. That means 3, 6, 9, ...... infinite will be part of the set P. So the answer to the question "is every positive multiple
of 3 in P" is affirmative. SUFFICIENT

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

It is already given in the question stem that 3 is in the set P. So this statement sets the trigger. That menas 0, -3, -6, -9.... ....infinite will be in set P. So the answer to the question is negative. SUFFICIENT.

Intern
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But why assume that 3 is the only member in the set?

thats my prob.
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sudzpwc wrote:
But why assume that 3 is the only member in the set?

thats my prob.

sudzpwc,

We are not assuming that 3 is the only member in the set P. There could be other integers in the set P. But in the question stem (not in the statements), it is given that 3 is the part of P. So you have to accept that 3 is member of P and then consider each statment.

Hope this helps
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A?

because using 2 we can say that every multiple of 3 might be or might not be in the set.
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jaydi8 wrote:
A?

because using 2 we can say that every multiple of 3 might be or might not be in the set.

YES. I think you are right. Based on statement 2 alone we can not say anything definitely.

Stolyar, do you agree with this?

I think the answer should be A. Thanks jaydi8.
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Am,
get your point now.Thanks for the help.appreciate it.
god luck.
sudz
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The question asked "Are all positive multiples of 3 in P?". With statement (II) 3, 0, -3, -6 ..... i.e. every positive multiple of 3 isn't in P.Hence the statement is sufficient.
IMO, D is the correct choice.
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Soumala wrote:
The question asked "Are all positive multiples of 3 in P?". With statement (II) 3, 0, -3, -6 ..... i.e. every positive multiple of 3 isn't in P.Hence the statement is sufficient.
IMO, D is the correct choice.

This is tricky. Here you have unknowingly assumed that 3 is the starting point. Now for the time being imagin that set P contains infinite integers in such a way that it fulfills the condition of statement II. For example start from 999. Then 999, 996, 993......3, 0, -3, -6,.....
all are in set P. Here I have used 999 as a starting point just to as an example. It could be an infinite number. IN that the answer to the question would be YES.

So the stament II can result in YES as well as NO. NOT SUFF.

IMO, the answer should be A.

Guys, please let me know what you think.
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Soumala wrote:
The question asked "Are all positive multiples of 3 in P?". With statement (II) 3, 0, -3, -6 ..... i.e. every positive multiple of 3 isn't in P.Hence the statement is sufficient.
IMO, D is the correct choice.

No. You only know what MUST be in, but not what actually is. Suppose P is the set of ALL integers? Then every positive multiple of 3 IS in P.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Let's try again

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.
3 is in, so 6, 9, 12, ... so on are in as well --- SUFF

(2) For any integer in P, that integer minus 3 is also in P.
3 is in, so 0, -3, -6, -9, ... so on are in as well --- can we say something different about POSITIVE multiples? They can be in P, and they can be not.

D is not correct, my fault.
It looks like A.
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