Number Properties

jtsgmat · Posted: Tue Jul 18, 2006 5:22 am Post subject: Number Properties

Does anyone know how to solve this?

If P is a set of integers and 3 is in P, is evervy positive multipe of 3 in P?

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

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

AD
BCE

Jason

lan0583 · Posted: Tue Jul 18, 2006 5:31 am Post subject:

I believe that the answer is E. Here's how I got the answer.

A. INSUFFICIENT: 3+1=4 which is not a multiple of 3, however, 3+3 is multiple of 3.
B. INSUFFICIENT: 6-3= 3 which is a multiple of 3, however, 2-3 is not a multiple of 3.

D. CANNOT BE: Because if we combined the two statements, it does not say anything about the answer. It always comes down to having two or more different answers.

I dont know if I am right but that's how I analyzed the problem.

joedinan · Posted: Fri Jul 21, 2006 8:36 pm Post subject: Re: Number Properties

rehanaj · Posted: Fri Jul 21, 2006 9:59 pm Post subject:

The answer could be A depending upon the interpretation of the problem.

In another interpretation of the problem, the answer could be (C).

I just took the set like {-3, 0 3}

I looked at statement (1)
-3 + 3 = 0 is in the set
0 + 3 is in the set
3 + 3 should be there as well, so set should be {-3, 0 , 3 , 6}
So you could go ad infinitum to show that the set is really {-3, 0, 3, 6, ...+infinity}
Sufficient

Then I looked at statement 2, Again started with {-3,0,3} backwards
3 - 3 = 0 is in the set
0 - 3 = -3 is in the set
-3 - 3 = -6 should also be there, so set should be {-6, -3, 0, 3}
So you could go ad infinitum to show that the set is really {-infinity, ...-3, 0, 3}

OK, so Statement 2 tells me that all positive multiples of 3 are not in P, UNLESS P already has ALL positive multiples of 3. That is, a situation like

{-infinity, ..., -3, 0, 3, 6, ....+infinity}

If that were not the case, I could argue that Statement 2 is ALSO SUFFICIENT TO TELL ME THAT THE SET WOULD NOT CONTAIN ALL +VE MULTIPLES OF 3. In this interpretation, Statement (2) is also SUFFICIENT.

But given that "infinity" itself is an ethereal concept, take your pick!

Rehana

yogeshsheth · Posted: Sun Sep 03, 2006 5:04 am Post subject:

My Pick would be A

As per statement 1 if 3 is there then all postive multiples of 3 will be there so it is sufficient.
As per statement 2 you can definately say that all negative multiples of 3 are present but nothing concrete can be said about positive multiples of 3. So statement 2 is insufficient.

So my pick is A

kulksnikhil · Posted: Tue Nov 14, 2006 11:09 pm Post subject: Re: Number Properties

gmat_enthus · Posted: Fri Nov 24, 2006 1:51 pm Post subject: Re: Number Properties