Data Sufficiency - Integers Question

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

IMO - E

Set could be - 0, 3, 6, 9 or 0, 1, 2, 3, 4, 5

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?

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!

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?

Thanks for all the help on this question guys. In particular, thank you Stuart for the thorough explainations. Its all very helpful!