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If P is a set of integers and 3 is in P, is every positive [#permalink]
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01 Oct 2003, 16:43
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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
Joined: 13 Sep 2003
Posts: 43
Location: US

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???



Manager
Joined: 11 Mar 2003
Posts: 54
Location: Chicago

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.
Answer D



Intern
Joined: 13 Sep 2003
Posts: 43
Location: US

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



Manager
Joined: 11 Mar 2003
Posts: 54
Location: Chicago

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



Intern
Joined: 10 Oct 2003
Posts: 45
Location: Finland

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



Manager
Joined: 11 Mar 2003
Posts: 54
Location: Chicago

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.



Intern
Joined: 13 Sep 2003
Posts: 43
Location: US

Am,
get your point now.Thanks for the help.appreciate it.
god luck.
sudz



Intern
Joined: 21 Jul 2003
Posts: 41
Location: India

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.



Senior Manager
Joined: 11 Nov 2003
Posts: 356
Location: Illinois

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.



GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE

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.
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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



SVP
Joined: 03 Feb 2003
Posts: 1604

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.










