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. 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.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 10 Jun 2010
Posts: 3

If P is a set of integers and 3 is in P, is every positive
[#permalink]
Show Tags
02 Jul 2010, 09:24
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.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 51100

If P is a set of integers and 3 is in P, is every positive
[#permalink]
Show Tags
02 Jul 2010, 10:01
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 \(x3\) > we know 3 is in P, hence \(33=0\) is also in and as 0 is in, so is \(03=3\), 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? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 03 May 2010
Posts: 85
WE 1: 2 yrs  Oilfield Service

Re: If P is a set of integers and 3 is in P, is every positive
[#permalink]
Show Tags
02 Jul 2010, 10:00
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, "q3" is also in P.
Since we know that 3 is in P, 33 = 0 is also in P Since we know that 0 is in P, 03 = 3 is also in P. Since we know that 3 is in P, 33 = 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.




Manager
Joined: 05 Jun 2014
Posts: 62

Re: If P is a set of integers and 3 is in P, is every positive
[#permalink]
Show Tags
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
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
21 Oct 2014, 02:06
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 \(x3\) > we know 3 is in P, hence \(33=0\) is also in and as 0 is in, so is \(03=3\), 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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 05 Jun 2014
Posts: 62

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



Intern
Joined: 31 Jul 2013
Posts: 15
Location: Viet Nam
Concentration: General Management, Entrepreneurship
GPA: 3.46
WE: Sales (Computer Software)

Re: If P is a set of integers and 3 is in P, is every positive
[#permalink]
Show Tags
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 \(x3\) > we know 3 is in P, hence \(33=0\) is also in and as 0 is in, so is \(03=3\), 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
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
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 \(x3\) > we know 3 is in P, hence \(33=0\) is also in and as 0 is in, so is \(03=3\), 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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 21 Oct 2017
Posts: 81
Location: France
Concentration: Entrepreneurship, Technology
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
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
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
02 Dec 2017, 22:32



Manager
Joined: 21 Oct 2017
Posts: 81
Location: France
Concentration: Entrepreneurship, Technology
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
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
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
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
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
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/foracertai ... 36580.htmlhttps://gmatclub.com/forum/asetofnum ... 98829.htmlhttps://gmatclub.com/forum/kisaseto ... 03005.htmlhttps://gmatclub.com/forum/kisaseto ... 96907.htmlhttp://gmatclub.com/forum/foracertain ... 36580.htmlhttps://gmatclub.com/forum/foracertai ... 61920.htmlHope 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? Extrahard Quant Tests with Brilliant Analytics



Intern
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
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/foracertai ... 36580.htmlhttps://gmatclub.com/forum/asetofnum ... 98829.htmlhttps://gmatclub.com/forum/kisaseto ... 03005.htmlhttps://gmatclub.com/forum/kisaseto ... 96907.htmlhttp://gmatclub.com/forum/foracertain ... 36580.htmlhttps://gmatclub.com/forum/foracertai ... 61920.htmlHope 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
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
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/foracertai ... 36580.htmlhttps://gmatclub.com/forum/asetofnum ... 98829.htmlhttps://gmatclub.com/forum/kisaseto ... 03005.htmlhttps://gmatclub.com/forum/kisaseto ... 96907.htmlhttp://gmatclub.com/forum/foracertain ... 36580.htmlhttps://gmatclub.com/forum/foracertai ... 61920.htmlHope 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? Extrahard Quant Tests with Brilliant Analytics



Intern
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
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
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
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? Extrahard Quant Tests with Brilliant Analytics



Intern
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
14 Dec 2017, 10:57
You are right, bunuel!



Manager
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
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. BunuelI am not clear how 2nd statement is insufficient. According to me second statement should be sufficient as it has all the elements that are Element3, 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
Joined: 21 Aug 2013
Posts: 1412
Location: India

Re: If P is a set of integers and 3 is in P, is every positive
[#permalink]
Show Tags
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. BunuelI am not clear how 2nd statement is insufficient. According to me second statement should be sufficient as it has all the elements that are Element3, 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 deviceHi 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.




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 ]



