bupbebeo wrote:IF P is a set of integer and # 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 , that integer minus 3 is also in P

Statement (1)

Suppose x = integer in set P .

Then x + 3 is in P .

Now x + 3 may be a multiple of 3 may not be .

Not sufficient .

Statement (2)

Suppose x = integer in set P .

Then x - 3 is in P .

Now x - 3 may be a multiple of 3 may not be .

Not sufficient .


Combine (1) and (2)

Now if you take any multiple of 3 and add or subtract 3 from it you will always get a multiple of 3 .

That is = > x (mul of 3)+/- 3 = y (mul of 3) . Y = integer .


This is in fact true for any integer

x (mul of A)+/- A = y (mul of A)

Here x , y and A are all integers .

Set P consists entirely of multiples of 3 only .

Ans C

Is 3 considered in P?

3 could be in P too right? Then st 2 would be zero for int=3.

How does it satisfy 1+2? I'm quite confused.

dxgamez wrote:Is 3 considered in P?

3 could be in P too right? Then st 2 would be zero for int=3.

How does it satisfy 1+2? I'm quite confused.

Why would you do 1+2 ?

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

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

You need to add or sub 3 from an integer .

Hey rockeyb do clarify this

You stated that

Now if you take any multiple of 3 and add or subtract 3 from it you will always get a multiple of 3 .

That is = > x (mul of 3)+/- 3 = y (mul of 3) . Y = integer .

How can you conclude that a number picked from set is multiple of 3.
If there is number 8 in the set
8-5 = 5
and 8=3 = 11
are also there but they arent multiples
Do clarify
I thought answer should be E

rockeyb wrote:

dxgamez wrote:Is 3 considered in P?

3 could be in P too right? Then st 2 would be zero for int=3.

How does it satisfy 1+2? I'm quite confused.

Why would you do 1+2 ?

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

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

You need to add or sub 3 from an integer .

From the book I read, i says the correct answer is A. Could everyone help us to explain why the correct answer is A.

You have stated the question wrong bupbebo. The question is

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

You wrote # instead of 3.

Nevertheless i shall explain now

Statement 1- Since the number 3 is in the set, so will 3+3 = 6 ans since 6 is there in the set now so will 6+3 = 9. That means the set contains an A.P with 3 as first term and 3 as difference. This A.P contains all the multiples of 3. Hence sufficent

Statement 2- This does not prove anything as we are looking for positive multiples of 3 not negative. Not sufficient

Hence answer is A

WOW !!!!

Thanks eaakbari you are a savior .

If we were not looking for +ve multiples of 3 then C should be the answer .

I hope you got that point .

Haha. Trying to get till where you are rockeyb.
Oh yes thats a good point. I might have slipped up.
Thanks

Whats the source any ways ?

nice save. that last amount of information (that 3 is in P) is super important.

@eaakbari: i do agree that without the new information, the answer should be E and the reason why is we just don't know if 3 is in the set, or if 0 is in the set, or any multiple of 3 is in the set. in order to confirm the question, we must have some knowledge of the elements in P.

Exactly I do feel the same. What do you say rockeyb?

eaakbari wrote:Exactly I do feel the same. What do you say rockeyb?

Lets say the question was changed to :

IF P is a set of integer , is every 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 , that integer minus 3 is also in P

Then in that case my answer would be C and not E .

Why? see my explanation above .

Lets say the question was changed to :

IF P is a set of integer , is every 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 , that integer minus 3 is also in P

Then in that case my answer would be C and not E .

Why? see my explanation above .

I would say E is correct answer.

Why do you say so ? Can you please explain.