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If P is a set of integers and 3 is in P, is every positive

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If P is a set of integers and 3 is in P, is every positive [#permalink]

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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.
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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We can write P as a set of an undetermined number of integers that contains the number 3.

P = {l , m , n, ..... , 3 , x , y , z, ....}

Is every positive multiple of 3 in P ?
In effect the question is asking you is every number in this infinite series : 3,6,9,12,15,....... is present in P, or not. A yes or no answer will suffice.

Statement 1:

For any integer "q" in P, "q+3" is also in P.

Since we know that 3 is in P, 3+3 = 6 is also in P.
Since we know that 6 is in P, 6+3 = 9 is also in P.
Since we know that 9 is in P, 9+3 = 12 is also in P.
AND SO ON....
Clearly this will go on forever, ensuring that EVERY positive multiple of 3 is in P. ANSWER to PROMPT - Yes

SUFFICIENT.

Statement 2:

For any integer "q" in P, "q-3" is also in P.

Since we know that 3 is in P, 3-3 = 0 is also in P
Since we know that 0 is in P, 0-3 = -3 is also in P.
Since we know that -3 is in P, -3-3 = -6 is also in P.
AND SO ON....
Clearly this will go on forever, ensuring all NEGATIVE multiples of 3 are in P.

What can we say about the POSITIVE multiples, remember an answer of No will suffice, but CAREFUL:

Two things:
1. 2 statements will never contradict eachother, so either this one is going to answer the question as "yes" just as Statement 1 did, or it is going to be insufficient. Since we don't seem to reach a clear yes, it is probably insufficient.

2. We don't know what other numbers were in the set P other than 3. Consider that P contained the highest positive multiple of 3. This is ofcourse a hypothetical situation since this number would be akin to infinity. But it is theoretically possible that this set contained that maximum positive multiple of 3. Thus, stepping down by 3 from this number as we have above, would result in obtaining all positive multiples of 3. Thus it is possible, but we cannot be sure of this fact from statement 2 since we do not know if this hypothetical number exists in the set or not.

ANSWER TO PROMPT: Maybe.
INSUFFICIENT.

Pick A.
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If P is a set of integers and 3 is in P, is every positive [#permalink]

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Caffmeister 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.


I had difficulty with this question because of the wording, I wasn't sure what they were looking for exactly, and I didn't find the explanation in the book to be sufficient. If anyone can break it down into an easier explanation I'd apprecaite it.


If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

Positive multiples of 3 are: 3, 6, 9, 12, 15, ... The question asks whether ALL these numbers are in the set P, taking into account that 3 is in this set.

(1) For any integer in P, the sum of 3 and that integer is also in P --> if \(x\) is in the set, so is \(x+3\) --> we know 3 is in P, hence \(3+3=6\) is also in, and as 6 is in so is \(6+3=9\), and so on. Which means that ALL positive multiples of 3 are in the set P. Sufficient.

Side note: above does not mean that only positive multiples of 3 are in P, there can be other numbers but we are only interested in them.

(2) For any integer in P, that integer minus 3 is also in P --> if \(x\) is in the set, so is \(x-3\) --> we know 3 is in P, hence \(3-3=0\) is also in and as 0 is in, so is \(0-3=-3\), and so on. So we are not sure whether all positive multiples of 3 are in P, all we know that there will be following numbers: 3, 0, -3, -6, -9, -12, ... Not sufficient.

Answer: A.

Hope it's clear.
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 21 Oct 2014, 01:54
Bunuel plz help. I m stuck here, how does st (1) ensure that just +ve multiples of 3 are in set P? For instance if it has -6, than 3 + -6 =-3, is also in that set, so the statement holds true but it has -ve multiples within the set. So I answered E due to the condition of "+ve multiples"
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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sunaimshadmani wrote:
Bunuel plz help. I m stuck here, how does st (1) ensure that just +ve multiples of 3 are in set P? For instance if it has -6, than 3 + -6 =-3, is also in that set, so the statement holds true but it has -ve multiples within the set. So I answered E due to the condition of "+ve multiples"


Please pay attention to the part in red:
If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

Positive multiples of 3 are: 3, 6, 9, 12, 15, ... The question asks whether ALL these numbers are in the set P, taking into account that 3 is in this set.

(1) For any integer in P, the sum of 3 and that integer is also in P --> if \(x\) is in the set, so is \(x+3\) --> we know 3 is in P, hence \(3+3=6\) is also in, and as 6 is in so is \(6+3=9\), and so on. Which means that ALL positive multiples of 3 are in the set P. Sufficient.

Side note: above does not mean that only positive multiples of 3 are in P, there can be other numbers but we are only interested in them.

(2) For any integer in P, that integer minus 3 is also in P --> if \(x\) is in the set, so is \(x-3\) --> we know 3 is in P, hence \(3-3=0\) is also in and as 0 is in, so is \(0-3=-3\), and so on. So we are not sure whether all positive multiples of 3 are in P, all we know that there will be following numbers: 3, 0, -3, -6, -9, -12, ... Not sufficient.

Answer: A.

The question does NOT ask whether P consists ONLY of positive multiples of 3. It asks whether every positive multiple of 3 in P.
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 21 Oct 2014, 02:33
Thanks. The last line made it crystal clear :)
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 02 Sep 2017, 20:46
Bunuel wrote:
Caffmeister 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.


I had difficulty with this question because of the wording, I wasn't sure what they were looking for exactly, and I didn't find the explanation in the book to be sufficient. If anyone can break it down into an easier explanation I'd apprecaite it.


If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

Positive multiples of 3 are: 3, 6, 9, 12, 15, ... The question asks whether ALL these numbers are in the set P, taking into account that 3 is in this set.

(1) For any integer in P, the sum of 3 and that integer is also in P --> if \(x\) is in the set, so is \(x+3\) --> we know 3 is in P, hence \(3+3=6\) is also in, and as 6 is in so is \(6+3=9\), and so on. Which means that ALL positive multiples of 3 are in the set P. Sufficient.

Side note: above does not mean that only positive multiples of 3 are in P, there can be other numbers but we are only interested in them.

(2) For any integer in P, that integer minus 3 is also in P --> if \(x\) is in the set, so is \(x-3\) --> we know 3 is in P, hence \(3-3=0\) is also in and as 0 is in, so is \(0-3=-3\), and so on. So we are not sure whether all positive multiples of 3 are in P, all we know that there will be following numbers: 3, 0, -3, -6, -9, -12, ... Not sufficient.

Answer: A.

Hope it's clear.


I'm not very clear with this answer. If your statement 2 can state like that, how didn't you question statement 1 in the same way? It means that we're not sure about whether set P contains min number like 0, 3, 6. Set P can start from 500 for example. In that case not every multiple of 3 is in the set P. Insufficient
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 03 Sep 2017, 03:46
hoangphuc wrote:
Bunuel wrote:
Caffmeister 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.


I had difficulty with this question because of the wording, I wasn't sure what they were looking for exactly, and I didn't find the explanation in the book to be sufficient. If anyone can break it down into an easier explanation I'd apprecaite it.


If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

Positive multiples of 3 are: 3, 6, 9, 12, 15, ... The question asks whether ALL these numbers are in the set P, taking into account that 3 is in this set.

(1) For any integer in P, the sum of 3 and that integer is also in P --> if \(x\) is in the set, so is \(x+3\) --> we know 3 is in P, hence \(3+3=6\) is also in, and as 6 is in so is \(6+3=9\), and so on. Which means that ALL positive multiples of 3 are in the set P. Sufficient.

Side note: above does not mean that only positive multiples of 3 are in P, there can be other numbers but we are only interested in them.

(2) For any integer in P, that integer minus 3 is also in P --> if \(x\) is in the set, so is \(x-3\) --> we know 3 is in P, hence \(3-3=0\) is also in and as 0 is in, so is \(0-3=-3\), and so on. So we are not sure whether all positive multiples of 3 are in P, all we know that there will be following numbers: 3, 0, -3, -6, -9, -12, ... Not sufficient.

Answer: A.

Hope it's clear.


I'm not very clear with this answer. If your statement 2 can state like that, how didn't you question statement 1 in the same way? It means that we're not sure about whether set P contains min number like 0, 3, 6. Set P can start from 500 for example. In that case not every multiple of 3 is in the set P. Insufficient


We know that 3 is in the set. From (1) we also know that if any integer is in the set, then (that integer) + 3 is also in the set. Since 3 is in the set, then so must be 3 + 3 = 6. If 6 is in the set, then so must be 6 + 3 = 9, and so on.
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 02 Dec 2017, 15:54
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.

----

I answered (E) because I read the question as asking "are all positive multiple of 3 in set P"? Meaning there is an infinity of positive multiples of 3, and we don't know if set P is infinite. Probably my understanding of English playing tricks on me. :?

Can anyone help me untangle this?

Thanks!
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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Hadrienlbb 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.

----

I answered (E) because I read the question as asking "are all positive multiple of 3 in set P"? Meaning there is an infinity of positive multiples of 3, and we don't know if set P is infinite. Probably my understanding of English playing tricks on me. :?

Can anyone help me untangle this?

Thanks!


If you read the first statement carefully you should understand that it implies that set P is infinite. Solution HERE makes it quite clear.
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 03 Dec 2017, 09:39
Bunuel wrote:
Hadrienlbb 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.

----

I answered (E) because I read the question as asking "are all positive multiple of 3 in set P"? Meaning there is an infinity of positive multiples of 3, and we don't know if set P is infinite. Probably my understanding of English playing tricks on me. :?

Can anyone help me untangle this?

Thanks!


If you read the first statement carefully you should understand that it implies that set P is infinite. Solution HERE makes it quite clear.


Yes, for any integer k in P, 3+k is also in P. So P is infinite.

Much clearer now. Thanks for pointing me to the right detail!
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 12 Dec 2017, 19:46
Hi Bunnel,

I understand how A is right, but I think B should also works fine. Because the second statement clearly mentions for every
Integer minus three results in that set. So now for. the given question 3 is already present, and that we need 6 in the set to get the result 3. So we only need multiples of 3 in positives too.
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 12 Dec 2017, 20:05
gvrk_77 wrote:
Hi Bunnel,

I understand how A is right, but I think B should also works fine. Because the second statement clearly mentions for every
Integer minus three results in that set. So now for. the given question 3 is already present, and that we need 6 in the set to get the result 3. So we only need multiples of 3 in positives too.


Not so. You cannot say that if 3 is there than 6 must also be there. What if the set is {3, 0, -3, -6, -9, -12, ... } So, basically what if 3 is the source integer?

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https://gmatclub.com/forum/for-a-certai ... 36580.html
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http://gmatclub.com/forum/for-a-certain ... 36580.html
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Hope this helps.
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 13 Dec 2017, 22:35
Bunuel wrote:
gvrk_77 wrote:
Hi Bunnel,

I understand how A is right, but I think B should also works fine. Because the second statement clearly mentions for every
Integer minus three results in that set. So now for. the given question 3 is already present, and that we need 6 in the set to get the result 3. So we only need multiples of 3 in positives too.


Not so. You cannot say that if 3 is there than 6 must also be there. What if the set is {3, 0, -3, -6, -9, -12, ... } So, basically what if 3 is the source integer?

Similar questions to practice:
https://gmatclub.com/forum/for-a-certai ... 36580.html
https://gmatclub.com/forum/a-set-of-num ... 98829.html
https://gmatclub.com/forum/k-is-a-set-o ... 03005.html
https://gmatclub.com/forum/k-is-a-set-o ... 96907.html
http://gmatclub.com/forum/for-a-certain ... 36580.html
https://gmatclub.com/forum/for-a-certai ... 61920.html


Hope this helps.




Hi bunnel,
So now as you’ve mentioned that what if the set consists of {3, 0, -3, -6, -9, -12, ... } is possible solution, then there is only one positive number which is multiple of 3 and that itself will satisfy the condition. We can’t write the set as {3, 2, 1, 0, -3, -6, -9, -12, ... }. Please help what I’m missing

Thanks,
Rajesh
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 13 Dec 2017, 22:50
gvrk_77 wrote:
Bunuel wrote:
gvrk_77 wrote:
Hi Bunnel,

I understand how A is right, but I think B should also works fine. Because the second statement clearly mentions for every
Integer minus three results in that set. So now for. the given question 3 is already present, and that we need 6 in the set to get the result 3. So we only need multiples of 3 in positives too.


Not so. You cannot say that if 3 is there than 6 must also be there. What if the set is {3, 0, -3, -6, -9, -12, ... } So, basically what if 3 is the source integer?

Similar questions to practice:
https://gmatclub.com/forum/for-a-certai ... 36580.html
https://gmatclub.com/forum/a-set-of-num ... 98829.html
https://gmatclub.com/forum/k-is-a-set-o ... 03005.html
https://gmatclub.com/forum/k-is-a-set-o ... 96907.html
http://gmatclub.com/forum/for-a-certain ... 36580.html
https://gmatclub.com/forum/for-a-certai ... 61920.html


Hope this helps.




Hi bunnel,
So now as you’ve mentioned that what if the set consists of {3, 0, -3, -6, -9, -12, ... } is possible solution, then there is only one positive number which is multiple of 3 and that itself will satisfy the condition. We can’t write the set as {3,2, 1, 0, -3, -6, -9, -12, ... }. Please help what I’m missing

Thanks,
Rajesh


The question asks: is every positive multiple of 3 in P? So, basically the question asks whether 3, 6, 9, 12, 15, ... ALL positive multiple of 3 are is set P. It's certainly possible ALL of them to be in the set, if the set is {..., -12, -9, -6, -3, 0, 3, 6, 9, 12, ...} nothing prevents this set to be an actual one (answer YES) but it's also possible the set to be {3, 0, -3, -6, -9, -12, ... } (answer NO).
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 14 Dec 2017, 09:49
I would go for E as well...

Imagine that the set mentioned is the set of all integers:
[...,-3,-2,-1,0,1,2,3,...]
Or it is a set of integers n, where n = 0+3k or n = 1+3k, k being any intenger:
[...-4,-3,-1,0,2,3,5,...]

In this case, the set satisfy statement a and b, but not every number in the set is a multiple of 3
so statement a and b are insufficient
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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 14 Dec 2017, 09:54
patriciadfer wrote:
I would go for E as well...

Imagine that the set mentioned is the set of all integers:
[...,-3,-2,-1,0,1,2,3,...]
Or it is a set of integers n, where n = 0+3k or n = 1+3k, k being any intenger:
[...-4,-3,-1,0,2,3,5,...]

In this case, the set satisfy statement a and b, but not every number in the set is a multiple of 3
so statement a and b are insufficient


The question does not ask whether all the numbers in the set are multiple of 3. The question asks whether all positive multiples of 3 are in the set. The correct answer to the question is A, not E. Please read the discussion above carefully and follow the links provided.

Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If P is a set of integers and 3 is in P, is every positive [#permalink]

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New post 14 Dec 2017, 10:57
You are right, bunuel!
Re: If P is a set of integers and 3 is in P, is every positive   [#permalink] 14 Dec 2017, 10:57
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