Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 28 Jun 2016, 21:47

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

K is a set of numbers such that (i) If x is in K, then -x

Author Message
TAGS:

Hide Tags

Manager
Joined: 30 Mar 2010
Posts: 84
GMAT 1: 730 Q48 V42
Followers: 0

Kudos [?]: 22 [2] , given: 5

K is a set of numbers such that (i) If x is in K, then -x [#permalink]

Show Tags

07 Jul 2010, 15:48
2
KUDOS
14
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

70% (01:59) correct 30% (01:04) wrong based on 512 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

[Reveal] Spoiler:
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??
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Oct 2013, 06:32, edited 2 times in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 33547
Followers: 5945

Kudos [?]: 73773 [5] , given: 9903

Show Tags

07 Jul 2010, 17:07
5
KUDOS
Expert's post
4
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.

Hope it's clear.
_________________
Manager
Joined: 30 Mar 2010
Posts: 84
GMAT 1: 730 Q48 V42
Followers: 0

Kudos [?]: 22 [0], given: 5

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: 33547
Followers: 5945

Kudos [?]: 73773 [0], given: 9903

Show Tags

07 Jul 2010, 17:57
Expert's post
afyl128 wrote:
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

$$x$$ and $$y$$ just represent some different numbers in the set K. (ii) says that if two different numbers ($$x$$ and $$y$$) are in the set, then their product ($$xy$$) is also in the set.

For example: as we know that 2 and -2 (two different numbers) are in the set, then their product (-2*2=-4) must also be in the set.

Hope it helps.
_________________
Manager
Joined: 30 Mar 2010
Posts: 84
GMAT 1: 730 Q48 V42
Followers: 0

Kudos [?]: 22 [0], given: 5

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: 33547
Followers: 5945

Kudos [?]: 73773 [0], given: 9903

Show Tags

08 Jul 2010, 16:57
Expert's post
afyl128 wrote:
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.

Yes, for ANY two numbers in the set their product is also in the set.
_________________
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 155

Kudos [?]: 1485 [0], given: 376

Re: QR DS 70 Number properties set [#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".
_________________
Intern
Joined: 08 Apr 2010
Posts: 6
Location: United States
Concentration: General Management
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: QR DS 70 Number properties set [#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: 22
Followers: 0

Kudos [?]: 6 [0], given: 5

Re: QR DS 70 Number properties set [#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: 147
Location: Italy
Concentration: General Management, Entrepreneurship
GMAT 1: 560 Q36 V34
GPA: 3.1
WE: Sales (Transportation)
Followers: 4

Kudos [?]: 6 [1] , given: 85

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
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

Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 547
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 50 [0], given: 562

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/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Math Expert
Joined: 02 Sep 2009
Posts: 33547
Followers: 5945

Kudos [?]: 73773 [1] , given: 9903

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
1
KUDOS
Expert's post
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.
_________________
Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 547
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 50 [0], given: 562

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/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Math Expert
Joined: 02 Sep 2009
Posts: 33547
Followers: 5945

Kudos [?]: 73773 [0], given: 9903

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
Expert's post
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.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6677
Location: Pune, India
Followers: 1832

Kudos [?]: 11150 [1] , given: 219

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
1
KUDOS
Expert's post
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 Current Student Joined: 26 Jul 2012 Posts: 63 Followers: 0 Kudos [?]: 8 [0], given: 8 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. Intern Joined: 17 Jun 2011 Posts: 6 Followers: 0 Kudos [?]: 0 [0], given: 0 OG-Q DS 70 [#permalink] Show Tags 29 Oct 2013, 06:18 Can someone give me an easier explanation of the solution? thanks Attachments Screen Shot 2013-10-29 at 9.14.00 pm.png [ 27.09 KiB | Viewed 6366 times ] Math Expert Joined: 02 Sep 2009 Posts: 33547 Followers: 5945 Kudos [?]: 73773 [0], given: 9903 Re: OG-Q DS 70 [#permalink] Show Tags 29 Oct 2013, 06:35 Expert's post 1 This post was BOOKMARKED zeallous wrote: Can someone give me an easier explanation of the solution? thanks Merging similar topics. Please ask if anything remains unclear. Similar questions to practice: a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html Hope this helps. _________________ Manager Joined: 15 Jan 2013 Posts: 58 Followers: 0 Kudos [?]: 22 [0], given: 10 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: 6677 Location: Pune, India Followers: 1832 Kudos [?]: 11150 [0], given: 219 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 Expert's post 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

Re: K is a set of numbers such that (i) If x is in K, then -x   [#permalink] 29 May 2014, 22:31

Go to page    1   2    Next  [ 26 posts ]

Similar topics Replies Last post
Similar
Topics:
9 If k is an integer and x(x – k) = k + 1, what is the value of x? 10 01 Sep 2015, 22:51
13 K is a set of numbers such that 8 30 Jan 2014, 23:48
K is a set of numbers such that: i. if x is in K, then -x is 7 16 Jun 2011, 14:01
K is a set of numbers such that... i) if x is in K, then -x 5 24 May 2011, 07:25
3 K is a set of numbers such that... i) if x is in K, then -x 6 12 May 2011, 14:47
Display posts from previous: Sort by