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

 It is currently 22 Aug 2019, 04:39 ### 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. ### Request Expert Reply # K is a set of numbers such that (i) If x is in K, then -x post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9551
Location: Pune, India
Re: K is a set of numbers such that (i) If x is in K, then -x  [#permalink]

### Show Tags

shagalo wrote:
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

Given:
(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
Stmnt 1: 2 is in K

This implies 2, -2, -4 (2*-2), -8 (2*-4), 8 (-2*-4), etc are in the set. 4 will not be there. But how do you know that no other elements are there in the set? Could we have a set like this: {12, 2, 24, -2, -12, -24 ...}
Does it satisfy all 3 conditions given above? Yes.
The set {2, -2, -4, -8, ...} satisfies all 3 conditions too.

Hence we don't know what the set actually looks like. Just because the set has 2 doesn't mean it cannot have 12.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Director  B
Joined: 03 Feb 2013
Posts: 837
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44 GPA: 3.88
WE: Engineering (Computer Software)
Re: K is a set of numbers such that (i) If x is in K, then -x  [#permalink]

### Show Tags

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

Statement 1) if 2 is in K, then -2 should be in K. Is 12 in K ? Not sufficient
Statement 2) Same as above not sufficient.

Both the statement) 2 is in K, then -2 is in K.
3 is in K, -3 is in K
2 and 3 both are in K, then 6 is in K

Till now we have K has {2,3,-2,-3,6}

Now as 6 is in K and also 2 is also in K, 12 has to be in K

Hence Sufficient - Option C)
_________________
Thanks,
Kinjal

My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961
Linkedin : https://www.linkedin.com/in/kinjal-das/

Please click on Kudos, if you think the post is helpful
Manager  S
Joined: 13 Mar 2013
Posts: 162
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)
Re: K is a set of numbers such that (i) If x is in K, then -x  [#permalink]

### Show Tags

Hi Bunuel,

Could please post the correct question . I think there is power missing in the main question here .
Please re-post the correct question .
_________________
Regards ,
Math Expert V
Joined: 02 Sep 2009
Posts: 57237
Re: K is a set of numbers such that (i) If x is in K, then -x  [#permalink]

### Show Tags

abhisheknandy08 wrote:
Hi Bunuel,

Could please post the correct question . I think there is power missing in the main question here .
Please re-post the correct question .

Nothing is missing there. The original question below:

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

_________________
Director  B
Joined: 04 Jun 2016
Posts: 558
GMAT 1: 750 Q49 V43 Re: K is a set of numbers such that (i) If x is in K, then -x  [#permalink]

### Show Tags

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
According to the restrictions if 2 (i.e " x") is in Set K then -2(i.e. "-x") should also be in Set K
since 2 and -2 are technically different numbers you can consider them x and y. Now (xy)= 2 * -2 = -4 should be there. Since -4 is there then its negative counterpart should be there too i.e "-(-4)" =4 and so on
K={2,-2, -4,4,-8,8,16,--16,32,-32,........}
Insufficient , we don not know apart from 2 and it's derivative what other numbers are inside Set K.

(2) 3 is in K
According to the restrictions if 3 is in k then -3 should also be in K
K={3,-3,-9,9,27,-27,81,-81.. } Insufficient , we do not know apart from 2 and it's derivative what other numbers are inside K

Merge both
K={2,-2,3,-3,4,-4,6,-6,12,-12,24,-24,27,-27...}

SUFFICIENT

ANSWER IS C
_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Originally posted by LogicGuru1 on 15 Jul 2016, 11:19.
Last edited by LogicGuru1 on 19 Sep 2016, 09:29, edited 1 time in total.
Intern  Joined: 07 Sep 2016
Posts: 20
Location: Brazil
Concentration: Sustainability, International Business
Schools: Rotman '19 (S)
GMAT 1: 590 Q43 V28 GPA: 2.95
WE: Account Management (Commercial Banking)
Re: K is a set of numbers such that (i) If x is in K, then -x  [#permalink]

### Show Tags

Bunuel wrote:
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.

When I was working on this questions I understood from statement 1+2 that 12 could be on the set. But as he asks: is 12 in the set? Well I assumed it could be in the set or not, why can I assume the set is not finite? I got a similar Gmat question wrong for assuming the opposite.
Math Expert V
Joined: 02 Sep 2009
Posts: 57237
Re: K is a set of numbers such that (i) If x is in K, then -x  [#permalink]

### Show Tags

Coruja wrote:
Bunuel wrote:
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.

When I was working on this questions I understood from statement 1+2 that 12 could be on the set. But as he asks: is 12 in the set? Well I assumed it could be in the set or not, why can I assume the set is not finite? I got a similar Gmat question wrong for assuming the opposite.

The stem gives clear description of the set and it's not saying that the set is finite.
_________________
Intern  B
Joined: 21 Jul 2015
Posts: 7
Re: K is a set of numbers such that (i) If x is in K, then -x  [#permalink]

### Show Tags

can someone please explain this question from the basic. i am not able to understand how is the set{....,-16,-8,-4,-2,2,4,8,16,....} or the set {....,-81,-27,-9,-3,3,9,27,81,...} is made.
Math Expert V
Joined: 02 Sep 2009
Posts: 57237
Re: K is a set of numbers such that (i) If x is in K, then -x  [#permalink]

### Show Tags Re: K is a set of numbers such that (i) If x is in K, then -x   [#permalink] 24 Dec 2017, 00:36

Go to page   Previous    1   2   [ 29 posts ]

Display posts from previous: Sort by

# K is a set of numbers such that (i) If x is in K, then -x post reply Question banks Downloads My Bookmarks Reviews Important topics

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

#### MBA Resources  