Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 30 Mar 2010
Posts: 82

K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
Updated on: 24 Dec 2017, 00:23
8
This post received KUDOS
24
This post was BOOKMARKED
Question Stats:
70% (00:58) correct 30% (01:03) wrong based on 904 sessions
HideShow timer Statistics
K is a set of numbers such that (i) If x is in K, then x is in K, and (ii) if each of x and y is in K, then xy is in K Is 12 in K? (1) 2 is in K (2) 3 is in K for (1) know that 2, 2 is in K for (2) know that 3, 3 is in K Together have [3, 2, 2, 3, 6]
So I would say neither is sufficient?? OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/kisaseto ... 66908.html
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by afyl128 on 07 Jul 2010, 15:48.
Last edited by Bunuel on 24 Dec 2017, 00:23, edited 4 times in total.
Edited the question



Math Expert
Joined: 02 Sep 2009
Posts: 45498

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
07 Jul 2010, 17:07
11
This post received KUDOS
Expert's post
11
This post was BOOKMARKED
afyl128 wrote: My First post K is a set of numbers such that (i) If x is in K, then x is in K, and (ii) if each of x and y is in K, then xy is in K Is 12 in K? (1) 2 is in K (2) 3 is in K for (1) know that 2, 2 is in K for (2) know that 3, 3 is in K Together have [3, 2, 2, 3, 6] So I would say neither is sufficient?? Hi, and welcome to the club. Below is the solution for your problem. (1) 2 is in K > according to (i) 2 is n K > according to (ii) 2*2=4 is in K > according to (i) (4)=4 is in K and so on. Thus we know that 2, 2, 4, 4, 8, 8, 16, 16, ... are in K, so basically powers of 2 and their negative pairs. Is 12 in K? We don't know. Not sufficient. (2) 3 is in K > according to (i) 3 is n K > according to (ii) 3*3=9 is in K > according to (i) (9)=9 is in K and so on. Thus we know that 3, 3, 9, 9, 27, 27, 81, 81, ... are in K, so basically powers of 3 and their negative pairs. Is 12 in K? We don't know. Not sufficient. (1)+(2) From (1) 4 is in K and from (2) 3 is in K, hence according to (ii) 4*3=12 must also be in K. Sufficient. Answer: C. 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: 30 Mar 2010
Posts: 82

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
07 Jul 2010, 17:47
Ahh I guess so but I'm having difficulty understanding why x * x is in the set because it states xy is in the set and not x* x everything else below made sense.
I'm just starting out so hopefully I get a better sense of these conditions as I progress
Posted from my mobile device



Math Expert
Joined: 02 Sep 2009
Posts: 45498

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
07 Jul 2010, 17:57



Manager
Joined: 30 Mar 2010
Posts: 82

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
08 Jul 2010, 15:32
many thanks for the responses!
Although I'm still missing something fundamental, if (2, 2 and 4) is in the set, why is (2 * 4 = 8 etc) in the set? As you mentioned below we know 2 numbers are in the set and the multiple of the two numbers. Is there wording in there that implies every number in the set can be multiplied by any other number in the set apart from just x or y. To me x, y and xy implies 3 values.



Math Expert
Joined: 02 Sep 2009
Posts: 45498

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
08 Jul 2010, 16:57



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1902

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
21 Feb 2011, 10:05
I. 2 is in k; 2,4,4,8,8,16,16. 12 is not there in this series. But, it may be there. II. 3 is in k; 3,3,9,9,27,27. 12 is not there in this series. But, it may be there. Using both; 2,3,2,3,4,9,6,6,12. 12 is definitely there. Ans: "C".
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 08 Apr 2010
Posts: 6
Location: United States
Concentration: General Management

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
12 Jun 2011, 12:50
fluke wrote: I. 2 is in k; 2,4,4,8,8,16,16. 12 is not there in this series. But, it may be there. II. 3 is in k; 3,3,9,9,27,27. 12 is not there in this series. But, it may be there.
Using both; 2,3,2,3,4,9,6,6,12. 12 is definitely there.
Ans: "C". Hi Fluke, The question asks us if '12 is in K'. After writing out the sequence (as Bunnel has done), I was NOT able to get a 12. Therefore, my answer was suffcient, because I could answer definitively and say that 12 is NOT in K. I reached the same conclusion with statement (2). Therefore, my answer to this question was D. In your quote above you mention that "[12] may be there". This is what I do not understand. If the statement given to us is a fact, then how can we assume that the sequence COULD have a 12 ? (even after we draw out the set and no 12 is present) Bunnel, if you can, can you jump in on this one too please!



Intern
Joined: 24 May 2011
Posts: 19

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
11 Dec 2011, 03:55
ngbrian85 wrote: fluke wrote: I. 2 is in k; 2,4,4,8,8,16,16. 12 is not there in this series. But, it may be there. II. 3 is in k; 3,3,9,9,27,27. 12 is not there in this series. But, it may be there.
Using both; 2,3,2,3,4,9,6,6,12. 12 is definitely there.
Ans: "C". Hi Fluke, The question asks us if '12 is in K'. After writing out the sequence (as Bunnel has done), I was NOT able to get a 12. Therefore, my answer was suffcient, because I could answer definitively and say that 12 is NOT in K. I reached the same conclusion with statement (2). Therefore, my answer to this question was D. In your quote above you mention that "[12] may be there". This is what I do not understand. If the statement given to us is a fact, then how can we assume that the sequence COULD have a 12 ? (even after we draw out the set and no 12 is present) Bunnel, if you can, can you jump in on this one too please! For (i) the data that is given is just enough to say that powers of 2 are present in the set. Data is "INSUFFICIENT" to "DEFINITELY" say that 12 isn't there in the set. It could be so that 12 is present but it hasn't been mentioned. So we can't categorically rule out the presence of 12 in the set, and say NO to the question "Is 12 in K? " Same with (ii). The data given is "INSUFFICIENT" to say "DEFINITELY" that 12 isn't there. Taking i and ii together, we can DEFINITELY say with this data that 12 is present. ie the statements together are SUFFICIENT



Manager
Joined: 13 Feb 2012
Posts: 141
Location: Italy
Concentration: General Management, Entrepreneurship
GPA: 3.1
WE: Sales (Transportation)

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
05 Sep 2012, 03:37
1
This post received KUDOS
Just in case someone made my same mistake: always write down the numbers (ex. 2; 2; 4 and so on) in order to realize that you have to deal with a new number everytime you have one: if 2 is there, 2 is there; so 4 is there, so 4 is there and so on, just like Bunuel showed. I did not write down any of that and ended up with E. Kudos and thanks to Bunuel.
_________________
"The Burnout"  My Debrief
Kudos if I helped you
Andy



Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 483
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
16 Dec 2012, 00:54
bunuel, This is how I solved.. For 12 to be in the set, 2 and 3 must be there.. as 12's prime factors are 2 and 3.. hence C. Is this correct?
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Math Expert
Joined: 02 Sep 2009
Posts: 45498

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
16 Dec 2012, 08:14
Sachin9 wrote: bunuel,
This is how I solved..
For 12 to be in the set, 2 and 3 must be there.. as 12's prime factors are 2 and 3.. hence C. Is this correct? No, that's not correct. 12 can be in the set even if 2 and 3 are not. For example, (i) says that "if x is in K, then x is in K", then if we were told that 12 is in the set then (12)=12 would be in the set. Or, (ii) say that "if each of x and y is in K, then xy is in K", then if we were told that both 2 and 6 are in the set, then 2*6=12 would be in the set. Of course there are many other possibilities. 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



Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 483
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
16 Dec 2012, 20:58
Bunuel wrote: Sachin9 wrote: bunuel,
This is how I solved..
For 12 to be in the set, 2 and 3 must be there.. as 12's prime factors are 2 and 3.. hence C. Is this correct? No, that's not correct. 12 can be in the set even if 2 and 3 are not. For example, (i) says that "if x is in K, then x is in K", then if we were told that 12 is in the set then (12)=12 would be in the set. Or, (ii) say that "if each of x and y is in K, then xy is in K", then if we were told that both 2 and 6 are in the set, then 2*6=12 would be in the set. Of course there are many other possibilities. Hope it's clear. Yeah so, for 12 to be in the set, according to the given conditions, presence of 2 of the factors (other than 1) of 12 is required .. Since 2 and 3 are present, it follows that 12 will be there.. Is this correct?
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Math Expert
Joined: 02 Sep 2009
Posts: 45498

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
16 Dec 2012, 23:22
Sachin9 wrote: Bunuel wrote: Sachin9 wrote: bunuel,
This is how I solved..
For 12 to be in the set, 2 and 3 must be there.. as 12's prime factors are 2 and 3.. hence C. Is this correct? No, that's not correct. 12 can be in the set even if 2 and 3 are not. For example, (i) says that "if x is in K, then x is in K", then if we were told that 12 is in the set then (12)=12 would be in the set. Or, (ii) say that "if each of x and y is in K, then xy is in K", then if we were told that both 2 and 6 are in the set, then 2*6=12 would be in the set. Of course there are many other possibilities. Hope it's clear. Yeah so, for 12 to be in the set, according to the given conditions, presence of 2 of the factors (other than 1) of 12 is required .. Since 2 and 3 are present, it follows that 12 will be there.. Is this correct? The red part it not correct. In the post you are quoting you can see that 12 can be there if 12 is in the set.
_________________
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8078
Location: Pune, India

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
17 Dec 2012, 23:44
Sachin9 wrote: bunuel,
This is how I solved..
For 12 to be in the set, 2 and 3 must be there.. as 12's prime factors are 2 and 3.. hence C. Is this correct? Responding to a pm: Given in the question: (ii) if each of x and y is in K, then xy is in K What does this mean? It means that if x and y are in K, then xy must also be there e.g. x = 6, y = 8 If 6 and 8 are in K, 6*8 = 48 must also be in K. Does it also mean that 2 and 3 (i.e. factors of 6) must also be in K? No. It is not necessary. I am building the set K. I could have put 6 in on my own. I don't need to start from 2 and 3 necessarily. If 6 and 8 are in the set K, I necessarily need to put their product in too. But I needn't put in their prime factors. We do not know whether their prime factors were put in and hence 6 and 8 were obtained or whether they were put in by set maker's choice. So, the statement 'if each of x and y is in K, then xy is in K' only implies that product of x and y must be in K too. It doesn't imply that factors of x and y must be in K. x and y could have been put in by choice. Who says that only prime factors can be added to the set? You can pick any number and add it to the set. The only thing is that once you put in that number, you must put in its product with every number already there in the set and so on... As pointed out by Bunuel, I hope you see that your logic is not correct.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 26 Jul 2012
Posts: 63

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
13 Apr 2013, 08:31
Thank you Karishma. Your statement that we don't have to start with 2 or 3 to make the set was the KEY for me. It really told me that may be 12 is possible for statement 1 and 2 because earlier I thought it was ALWAYS NO and was wondering how one could get 12 in the set K. Of course, if we don't assume that we always have to start building the set with 2 or 3, then 12 is entirely possible. Since this is ALWAYS no or ALWAYS yes question, C makes much more sense now. VeritasPrepKarishma wrote: Sachin9 wrote: bunuel,
This is how I solved..
For 12 to be in the set, 2 and 3 must be there.. as 12's prime factors are 2 and 3.. hence C. Is this correct? Responding to a pm: Given in the question: (ii) if each of x and y is in K, then xy is in K What does this mean? It means that if x and y are in K, then xy must also be there e.g. x = 6, y = 8 If 6 and 8 are in K, 6*8 = 48 must also be in K. Does it also mean that 2 and 3 (i.e. factors of 6) must also be in K? No. It is not necessary. I am building the set K. I could have put 6 in on my own. I don't need to start from 2 and 3 necessarily. If 6 and 8 are in the set K, I necessarily need to put their product in too. But I needn't put in their prime factors. We do not know whether their prime factors were put in and hence 6 and 8 were obtained or whether they were put in by set maker's choice. So, the statement 'if each of x and y is in K, then xy is in K' only implies that product of x and y must be in K too. It doesn't imply that factors of x and y must be in K. x and y could have been put in by choice. Who says that only prime factors can be added to the set? You can pick any number and add it to the set. The only thing is that once you put in that number, you must put in its product with every number already there in the set and so on... As pointed out by Bunuel, I hope you see that your logic is not correct.



Math Expert
Joined: 02 Sep 2009
Posts: 45498

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
29 Oct 2013, 06:35
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED



Manager
Joined: 15 Jan 2013
Posts: 57

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
29 May 2014, 21:29
can any one tell me why (1) and (2) are insufficient ? (1) shows that the set is …. 16,8,4,,2,4,8,16….( there is no 12 here) so it is sufficient. (2) shows that the set is …. 27,9,3,3,9,27,…… ( there is no 12 here) so it is sufficient. so the answer is D … each alone is sufficient.
any explanation please? thanks



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8078
Location: Pune, India

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
29 May 2014, 22:31
shagalo wrote: can any one tell me why (1) and (2) are insufficient ? (1) shows that the set is …. 16,8,4,,2,4,8,16….( there is no 12 here) so it is sufficient. (2) shows that the set is …. 27,9,3,3,9,27,…… ( there is no 12 here) so it is sufficient. so the answer is D … each alone is sufficient.
any explanation please? thanks How does statement 1 show that 12 is not in the set? All statement 1 tells you is that 2 is there and hence 2 is there. We don't know anything about other elements. How did you get 4... We are not given that if 2 is there, only powers of 2 will be there.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 15 Jan 2013
Posts: 57

Re: K is a set of numbers such that (i) If x is in K, then x [#permalink]
Show Tags
29 May 2014, 22:40
VeritasPrepKarishma wrote: shagalo wrote: can any one tell me why (1) and (2) are insufficient ? (1) shows that the set is …. 16,8,4,,2,4,8,16….( there is no 12 here) so it is sufficient. (2) shows that the set is …. 27,9,3,3,9,27,…… ( there is no 12 here) so it is sufficient. so the answer is D … each alone is sufficient.
any explanation please? thanks How does statement 1 show that 12 is not in the set? All statement 1 tells you is that 2 is there and hence 2 is there. We don't know anything about other elements. How did you get 4, 8 etc. We are not given that if 2 is there, only powers of 2 will be there.  Sorry but your explanation is not clear. and i got these numbers " 16,8,4,,2,4,8,16…" after applying the statement (1) on the equation (i) and (ii). what i understood is that if you applied statement (1) "2 in K", then you will get this set of numbers " 16,8,4,,2,4,8,16…" which do not include 12. the same apply on statement (2). could you explain what is the flaw in my understanding. Thanks




Re: K is a set of numbers such that (i) If x is in K, then x
[#permalink]
29 May 2014, 22:40



Go to page
1 2
Next
[ 29 posts ]



