GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 11 Dec 2018, 14:37

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 10 Jun 2010
Posts: 3
If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

New post 02 Jul 2010, 09:24
3
24
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (01:37) correct 59% (01:50) wrong based on 659 sessions

HideShow timer Statistics

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.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

New post 02 Jul 2010, 10:01
8
5
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 03 May 2010
Posts: 85
WE 1: 2 yrs - Oilfield Service
Reviews Badge
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

New post 02 Jul 2010, 10:00
6
3
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.
General Discussion
Manager
Manager
avatar
Joined: 05 Jun 2014
Posts: 62
GMAT 1: 630 Q42 V35
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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"
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

New post 21 Oct 2014, 02:06
1
1
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 05 Jun 2014
Posts: 62
GMAT 1: 630 Q42 V35
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

New post 21 Oct 2014, 02:33
Thanks. The last line made it crystal clear :)
Intern
Intern
avatar
B
Joined: 31 Jul 2013
Posts: 15
Location: Viet Nam
Concentration: General Management, Entrepreneurship
GMAT 1: 650 Q49 V28
GPA: 3.46
WE: Sales (Computer Software)
GMAT ToolKit User
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
S
Joined: 21 Oct 2017
Posts: 81
Location: France
Concentration: Entrepreneurship, Technology
GMAT 1: 750 Q48 V44
GPA: 4
WE: Project Management (Internet and New Media)
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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!
_________________

Please Press +1 Kudos if it helps!

October 9th, 2017: Diagnostic Exam - Admit Master (GoGMAT) - 640
November 11th, 2017: CAT 1 - Admit Master (GoGMAT) - 700
November 20th, 2017: CAT 2 - GMATPrep - 700 (Q: 47, V: 40)
November 25th, 2017: CAT 3 - Admit Master (GoGMAT) - 710 (Q: 48, V: 40)
November 27th, 2017: CAT 4 - GMATPrep - 720 (Q: 49, V: 40)

December 4th, 2017: GMAT Exam - 750 (Q: 48, V: 44, IR: 8, AWA: 6)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

New post 02 Dec 2017, 22:32
1
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
S
Joined: 21 Oct 2017
Posts: 81
Location: France
Concentration: Entrepreneurship, Technology
GMAT 1: 750 Q48 V44
GPA: 4
WE: Project Management (Internet and New Media)
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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!
_________________

Please Press +1 Kudos if it helps!

October 9th, 2017: Diagnostic Exam - Admit Master (GoGMAT) - 640
November 11th, 2017: CAT 1 - Admit Master (GoGMAT) - 700
November 20th, 2017: CAT 2 - GMATPrep - 700 (Q: 47, V: 40)
November 25th, 2017: CAT 3 - Admit Master (GoGMAT) - 710 (Q: 48, V: 40)
November 27th, 2017: CAT 4 - GMATPrep - 720 (Q: 49, V: 40)

December 4th, 2017: GMAT Exam - 750 (Q: 48, V: 44, IR: 8, AWA: 6)

Intern
Intern
avatar
B
Joined: 23 Oct 2016
Posts: 17
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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?

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 23 Oct 2016
Posts: 17
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 03 Dec 2017
Posts: 5
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 03 Dec 2017
Posts: 5
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

New post 14 Dec 2017, 10:57
You are right, bunuel!
Manager
Manager
avatar
B
Joined: 29 Nov 2016
Posts: 53
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

New post 04 Mar 2018, 05:02
Bunuel wrote:
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.


Bunuel

I am not clear how 2nd statement is insufficient. According to me second statement should be sufficient as it has all the elements that are Element-3,

If there is an infinitely large number that is a multiple of 3 say 3333333333 then it will have 3333333330 in the set but it will not have 3333333336 in the set. If it has 3333333336 in the set it will not have 3333333339 in the set.

It does not guarantee that all positive multiple of 3 are there in the set as all positive multiple can tend to infinity.

Hence the statement 2 should be sufficient.

Posted from my mobile device
DS Forum Moderator
avatar
P
Joined: 21 Aug 2013
Posts: 1412
Location: India
Premium Member
Re: If P is a set of integers and 3 is in P, is every positive  [#permalink]

Show Tags

New post 04 Mar 2018, 06:23
Mudit27021988 wrote:
Bunuel wrote:
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.


Bunuel

I am not clear how 2nd statement is insufficient. According to me second statement should be sufficient as it has all the elements that are Element-3,

If there is an infinitely large number that is a multiple of 3 say 3333333333 then it will have 3333333330 in the set but it will not have 3333333336 in the set. If it has 3333333336 in the set it will not have 3333333339 in the set.

It does not guarantee that all positive multiple of 3 are there in the set as all positive multiple can tend to infinity.

Hence the statement 2 should be sufficient.

Posted from my mobile device



Hi

In your example, if 3333333333 is present, then its sure that 3333333330 is also present.
and now since 3333333330 is present, we are sure that 3333333327 is also present.
Similarly 3333333324, 3333333321, .........., 9, 3, 0, -3, -6, -9, .... are ALL present.

But we cannot be sure about multiples of 3 greater than 3333333333. 3333333336 might or might not be present. Statement 2 doesn't say that 'element + 3' cannot be present, it says that 'element - 3' has to be present.

So we cannot be sure whether ALL positive multiples of 3 are present or not.

Thats why statement 2 is NOT sufficient.
GMAT Club Bot
Re: If P is a set of integers and 3 is in P, is every positive &nbs [#permalink] 04 Mar 2018, 06:23

Go to page    1   2    Next  [ 23 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.