Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 29 May 2017, 16:53

### 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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106577 [0], given: 11628

K is a set of numbers such that [#permalink]

### Show Tags

30 Jan 2014, 23:48
Expert's post
15
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

67% (02:10) correct 33% (01:10) wrong based on 516 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

Data Sufficiency
Question: 70
Category: Arithmetic Properties of numbers
Page: 158
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106577 [0], given: 11628

Re: K is a set of numbers such that [#permalink]

### Show Tags

30 Jan 2014, 23:48
Expert's post
4
This post was
BOOKMARKED
SOLUTION

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 (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.

Similar questions to practice:
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-both-161920.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html

Hope this helps.
_________________
Manager
Joined: 23 Jun 2008
Posts: 85
Location: Australia
Schools: AGSM '22
GMAT Date: 04-01-2014
Followers: 1

Kudos [?]: 45 [0], given: 24

Re: K is a set of numbers such that [#permalink]

### Show Tags

31 Jan 2014, 01:08
Let's analyze statements with what's given in the question.

Statement (1)
2 is in K
(i) -2 is also in K
(ii) 2 and -2 are both in K, so -4 is also in K .... then +4... and then -8 and +8 are in K ... looks like 2^n and -2^n are included where n is integer
which does not include 12 definitely...
So Statement (1) is sufficient to answer the question "Is 12 in K?", answer being no.

Statement (2)
Similarly results in a set 3^n and -3^n , which again answers our question, that 12 is definitely not part of the set K.
So Statement (2 is sufficient to answer the question "Is 12 in K?", answer being no.

Answer D; Both statement 1 & statement 2 are ALONE sufficient.

[oops It turns out my answer was wrong ... Just leaving the post as it is, so you know what not to do ]
_________________

Kudos (+1) if you find this post helpful.

Last edited by code19 on 31 Jan 2014, 13:59, edited 4 times in total.
Senior Manager
Joined: 20 Dec 2013
Posts: 267
Location: India
Followers: 0

Kudos [?]: 89 [1] , given: 29

Re: K is a set of numbers such that [#permalink]

### Show Tags

31 Jan 2014, 01:59
1
KUDOS
Ans. C
From S1:if 2 is in the series,then -2 will also be there.
And if 2 & -2 are there -4 will be there.If -4 is in the series, 4 will also be there...and so on
The series becomes:2,-2,4,-4...powers of 2
But the stimulus remains silent about what is not there in this series.So insufficient.(12 might or might not be there.)

Same explanation for S2:The series will have numbers with powers of 3.

Together for S1 & S2,at some point we'll have multiple of 3 and 4 because if 3 and 4 are there in the series,their multiple will definitely be there as implied by the second statement in stimulus.Sufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106577 [0], given: 11628

Re: K is a set of numbers such that [#permalink]

### Show Tags

01 Feb 2014, 10:30
Expert's post
1
This post was
BOOKMARKED
SOLUTION

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 (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.

Similar questions to practice:
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-both-161920.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html

Hope this helps.
_________________
Intern
Joined: 27 Jan 2014
Posts: 7
Location: India
Concentration: General Management, Finance
Schools: HBS '16, Wharton '16
GMAT Date: 04-25-2014
GPA: 3.77
WE: Project Management (Investment Banking)
Followers: 0

Kudos [?]: 15 [0], given: 13

Re: K is a set of numbers such that [#permalink]

### Show Tags

19 Feb 2014, 07:01
Bunuel, one quick query -> When we say that (from stmt 1) 2 is there in the set and hence -2 is also there -> Here we take 2 and -2 as x and -x, but then we also apply the logic x*y = -4 (here we consider 2 as x and -2 as y (and not as -x)).
Could there be a flaw in the problem statement?

Bunuel wrote:
Bunel can you update the oa? It shows as d on gmat timer.

________________
Done. Thank you.
Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106577 [0], given: 11628

Re: K is a set of numbers such that [#permalink]

### Show Tags

19 Feb 2014, 07:52
sunnymon wrote:
Bunuel, one quick query -> When we say that (from stmt 1) 2 is there in the set and hence -2 is also there -> Here we take 2 and -2 as x and -x, but then we also apply the logic x*y = -4 (here we consider 2 as x and -2 as y (and not as -x)).
Could there be a flaw in the problem statement?

Bunuel wrote:
Bunel can you update the oa? It shows as d on gmat timer.

________________
Done. Thank you.

(i) and (ii) are general rules for the set, meaning that they apply to any numbers in the set:

(i) if a number is in K, then - that number is also in K
(ii) for any two numbers in the set, their product is also in the set.

Hope it's clear.
_________________
Manager
Joined: 26 Feb 2015
Posts: 127
Followers: 0

Kudos [?]: 15 [0], given: 43

K is a set of numbers such that [#permalink]

### Show Tags

22 Mar 2015, 03:23
What is unclear to me is that it states that xy is in the set, but how can we infer that x*x and y*y is in the set.

-2 and 2
-3 and 3 gives us 6? How can do we infer that -2 * 2 = 4 is in the set?
Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106577 [1] , given: 11628

Re: K is a set of numbers such that [#permalink]

### Show Tags

22 Mar 2015, 06:10
1
KUDOS
Expert's post
erikvm wrote:
What is unclear to me is that it states that xy is in the set, but how can we infer that x*x and y*y is in the set.

-2 and 2
-3 and 3 gives us 6? How can do we infer that -2 * 2 = 4 is in the set?

(i) and (ii) are general rules for the set, meaning that they apply to any numbers in the set:

(i) if a number is in K, then - that number is also in K
(ii) for any two numbers in the set, their product is also in the set.

(1) says that 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.

(2) says 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.

Does this make sense?
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15523
Followers: 651

Kudos [?]: 211 [0], given: 0

Re: K is a set of numbers such that [#permalink]

### Show Tags

25 Sep 2016, 06:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 11 Jan 2016
Posts: 35
Followers: 0

Kudos [?]: 1 [0], given: 32

K is a set of numbers such that [#permalink]

### Show Tags

29 Oct 2016, 04:55
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

Can you please explain the solution?

Last edited by Vyshak on 29 Oct 2016, 09:25, edited 1 time in total.
Topic Merged. Refer to the above discussions
VP
Joined: 12 Sep 2015
Posts: 1441
Followers: 139

Kudos [?]: 1645 [0], given: 329

K is a set of numbers such that [#permalink]

### Show Tags

29 Oct 2016, 09:29
Top Contributor
Oops - sorry. Looks like I was responding while Bunuel was merging topics.
_________________

Brent Hanneson – Founder of gmatprepnow.com

Senior Manager
Joined: 05 Jan 2017
Posts: 436
Location: India
Followers: 14

Kudos [?]: 43 [0], given: 15

Re: K is a set of numbers such that [#permalink]

### Show Tags

23 Feb 2017, 04:52
PROMPT ANALYSIS

Let us say that x and y are part of K
Hence K ={x,y,-x,-y,-xy,-y*y, -x*x….}

SUPERSET
The answer will be either YES or NO.

TRANSLATION
1# exact value of the element of K
2# some values to calculate the rest of the value

STATEMENT ANALYSIS

St 1: if 2 is in K, the -2 is in K, -4 is in K and so on. Hence, all the calculated elements will be in the form of 2n.we cannot say about rest of the element. Option a and d eliminated

St 2: if 3 is in K, the -3 is in K, -9 is in K and so on. Hence, all the calculated elements will be in the form of 3n.we cannot say about rest of the element.option b eliminated

St 1 & St 2: If 2 and 3 is in K, -2 and -3 is in K, -4 is also in K, 12 is in K.ANSWER

Option C
Intern
Joined: 06 May 2017
Posts: 3
Followers: 0

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

Re: K is a set of numbers such that [#permalink]

### Show Tags

06 May 2017, 09:18
Bunuel wrote:
SOLUTION

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 (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 this helps.

Hi Bunuel (or anyone else who can explain this),

In the sets mentioned above:
2, -2, -4, 4, 8, -8, 16, -16, ...
3, -3, -9, 9, 27, -27, 81, -81, ...

How are we getting 8, -8 in the first set and 27, -27 in the 2nd? Shouldn't it be 2,-2,-4,4,-16,16... and 3,-3,-9,9,-81,81...

The reason is that if we are taking xy as x and -x in statement (i), how do we get (for example) 8,-8 if we get -4 and 4 for x and -x? Is it that we are keeping y constant at 2 throughout? Please clarify.

Thanks.

Graeme
Math Expert
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106577 [0], given: 11628

Re: K is a set of numbers such that [#permalink]

### Show Tags

06 May 2017, 10:11
Graeme520 wrote:
Bunuel wrote:
SOLUTION

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 (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 this helps.

Hi Bunuel (or anyone else who can explain this),

In the sets mentioned above:
2, -2, -4, 4, 8, -8, 16, -16, ...
3, -3, -9, 9, 27, -27, 81, -81, ...

How are we getting 8, -8 in the first set and 27, -27 in the 2nd? Shouldn't it be 2,-2,-4,4,-16,16... and 3,-3,-9,9,-81,81...

The reason is that if we are taking xy as x and -x in statement (i), how do we get (for example) 8,-8 if we get -4 and 4 for x and -x? Is it that we are keeping y constant at 2 throughout? Please clarify.

Thanks.

Graeme

Next:
(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 --> according to (ii) 2*4 = 8 is in K --> according to (i) -8 is in K...

Hope it's clear.
_________________
Intern
Joined: 06 May 2017
Posts: 3
Followers: 0

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

Re: K is a set of numbers such that [#permalink]

### Show Tags

06 May 2017, 10:36
Bunuel wrote:
Graeme520 wrote:
Bunuel wrote:
SOLUTION

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 (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 this helps.

Hi Bunuel (or anyone else who can explain this),

In the sets mentioned above:
2, -2, -4, 4, 8, -8, 16, -16, ...
3, -3, -9, 9, 27, -27, 81, -81, ...

How are we getting 8, -8 in the first set and 27, -27 in the 2nd? Shouldn't it be 2,-2,-4,4,-16,16... and 3,-3,-9,9,-81,81...

The reason is that if we are taking xy as x and -x in statement (i), how do we get (for example) 8,-8 if we get -4 and 4 for x and -x? Is it that we are keeping y constant at 2 throughout? Please clarify.

Thanks.

Graeme

Next:
(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 --> according to (ii) 2*4 = 8 is in K --> according to (i) -8 is in K...

Hope it's clear.

Thanks for responding. Think I got it.

Therefore, we keep the pattern, substituting xy found in (ii) into "x" found in (i) but then, when coming back to (ii), leaving the original "x" = 2 in xy. Correct?
Re: K is a set of numbers such that   [#permalink] 06 May 2017, 10:36
Similar topics Replies Last post
Similar
Topics:
2 A set S contains five numbers k, k + 1, 2k - 1, 5k + 7 and 6k + 8. If 10 18 Jun 2015, 23:57
K is a set of numbers such that... i) if x is in K, then -x 5 14 Aug 2011, 23:49
3 K is a set of numbers such that... i) if x is in K, then -x 6 11 Apr 2012, 14:49
41 K is a set of numbers such that (i) If x is in K, then -x 28 18 Sep 2016, 09:30
7 Set K consists of a finite number of consecutive odd 9 30 Mar 2017, 23:34
Display posts from previous: Sort by