pappueshwar wrote: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.
OA IS A
why is statement 2 not sufficient ?
Hi pappueshwar!
Let's take a look at what we know from the stem. We have a set, and we only know that the number 3 is in that set.
Now, the question wants to know if all other POSITIVE multiples of 3 are in that set: 6, 9, 12, 15, .... Clear enough - let's jump in!
Statement 1: For any integer in P, the sum of 3 and that integer is also in P.
Well, we can only start with what we know: 3 is a number in the set. And it says, for any integers in the set, 3+that number is also in the set.
So if 3 is there, then 3+3=6 is there. Oh, so if 6 is there 3+6=9 is there. AH, and if 9 is there, 9+3=12 is there and so on and so on and so on! This means that ALL positive multiples of 3 are going to me in my set!
SUFFICIENT
Statement 2: For any integer in P, that integer minus 3 is also in P.
Well once again, we can only start with what we know: 3 is a number in the set. And it says, for any integers in the set, 3-that number is also in the set.
So if 3 is there, then 3-3=0 is there. Oh, so if 0 is there 0-3=-3 is there. AH, and if -3 is there, -3-3=-6 is there and so on and so on and so on! This means that ALL negative multiples of 3 are going to me in my set! But wait, what about the positive ones??
3 is the biggest (and only positive) number in the set that I am aware of, and I can't prove that there is anything bigger (I can only take what I know and apply it)
Take a look at this set:
{.....,-12,-9,-6,-3,0,3}
Is it true that for EVERY integer in the set, the integer #-3 is there as well?? It sure is, and there is only 1 positive multiple of 3 in there...
ameya85 wrote: as well as 0 which is not a multiple of 3.
Please note that 0 IS A multiple of 3...its actually a multiple of EVERY number (a multiple of 3 just must be able to be written in the form 3k where k is an integer - which can be k=0), it just isn't positive or negative!!
So, I don't know if EVERY positive multiple of 3 is going to be in there...[spoiler]NOT Sufficient![/spoiler]
Hope this clears up the confusion!
Whit
