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

It is currently 30 Apr 2016, 16:54
GMAT Club Tests

Close

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

S is a set of integers such that i) if a is in S, then –a

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 291
Location: India
Concentration: General Management, Entrepreneurship
Followers: 2

Kudos [?]: 185 [1] , given: 16

Reviews Badge
S is a set of integers such that i) if a is in S, then –a [#permalink]

Show Tags

New post 01 Apr 2012, 05:30
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

61% (01:47) correct 39% (01:08) wrong based on 214 sessions

HideShow timer Statictics

S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is –4 in S?

(1) 1 is in S.
(2) 2 is in S.
[Reveal] Spoiler: OA

_________________

Giving +1 kudos is a better way of saying 'Thank You'.

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5632

Kudos [?]: 68313 [1] , given: 9797

Re: S is a set of integers [#permalink]

Show Tags

New post 01 Apr 2012, 07:51
1
This post received
KUDOS
Expert's post
S is a set of integers such that i) if a is in S, then –a is in S, and ii) if each of a and b is in S, then ab is in S. Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Answer: B.

Similar questions:
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.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 it helps.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
avatar
Joined: 30 Apr 2011
Posts: 14
Followers: 0

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

Re: S is a set of integers [#permalink]

Show Tags

New post 02 Apr 2012, 18:46
Bunuel wrote:
S is a set of integers such that i) if a is in S, then –a is in S, and ii) if each of a and b is in S, then ab is in S. Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Answer: B.

Hope it helps.



How do you know that -a = b?
Senior Manager
Senior Manager
avatar
Joined: 10 Nov 2010
Posts: 266
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 189 [0], given: 22

Re: S is a set of integers [#permalink]

Show Tags

New post 03 Apr 2012, 02:23
bohdan01 wrote:
Bunuel wrote:
S is a set of integers such that i) if a is in S, then –a is in S, and ii) if each of a and b is in S, then ab is in S. Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Answer: B.

Hope it helps.



How do you know that -a = b?

we can interpret if a and b are two elements in the set then product of that two numbers will be in the set.so b is just another element in the set.

@Bunuel
Correct me if wrong
_________________

The proof of understanding is the ability to explain it.

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5632

Kudos [?]: 68313 [2] , given: 9797

Re: S is a set of integers [#permalink]

Show Tags

New post 03 Apr 2012, 04:48
2
This post received
KUDOS
Expert's post
bohdan01 wrote:
Bunuel wrote:
S is a set of integers such that i) if a is in S, then –a is in S, and ii) if each of a and b is in S, then ab is in S. Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Answer: B.

Hope it helps.



How do you know that -a = b?


We are told that: if some number a is in S, then –a is also in S, and if each of a and b is in S, then their product, ab is also in S.

(2) says that 2 is in S, then -2 also must be in S and since both 2 and -2 are in S then their product 2*(-2)=-4 must also be in S.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 235
Schools: Johnson '15
Followers: 2

Kudos [?]: 45 [0], given: 16

Re: S is a set of integers [#permalink]

Show Tags

New post 03 Apr 2012, 05:54
Bunuel wrote:
S is a set of integers such that i) if a is in S, then –a is in S, and ii) if each of a and b is in S, then ab is in S. Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Answer: B.

Similar questions:
og-quant-96907.html
ds-p-is-a-set-of-integers-96630.html
set-of-integers-103005.html

Hope it helps.



i agree with Bunuel's explanation.....the answer should be deduced using both the points given the question
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat ;)

Satyameva Jayate - Truth alone triumphs

Senior Manager
Senior Manager
avatar
Joined: 22 Dec 2011
Posts: 298
Followers: 3

Kudos [?]: 185 [0], given: 32

Re: S is a set of integers [#permalink]

Show Tags

New post 12 Oct 2012, 00:17
Bunuel wrote:
bohdan01 wrote:
Bunuel wrote:
S is a set of integers such that i) if a is in S, then –a is in S, and ii) if each of a and b is in S, then ab is in S. Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Answer: B.

Hope it helps.



How do you know that -a = b?


We are told that: if some number a is in S, then –a is also in S, and if each of a and b is in S, then their product, ab is also in S.

(2) says that 2 is in S, then -2 also must be in S and since both 2 and -2 are in S then their product 2*(-2)=-4 must also be in S.

Hope it's clear.



Bunuel - Im also confused, could you kindly help?
(2) says that 2 is in S so this can be a or b right?
So if 2 is a then -2 is -a
if 2 is b then -2 is -b
Aren't these mutually exclusive i.e how can we take 2 to be a and -2 to be b?

Also another way I (mistakenly) interpret the statements as if 2 (a or b) is in set then b (or a) can be any nos in the set? for example 5 then we cant get -4


please help!

cheers
1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 90

Kudos [?]: 760 [1] , given: 43

Re: S is a set of integers [#permalink]

Show Tags

New post 12 Oct 2012, 00:30
1
This post received
KUDOS
(2) says that 2 is in S so this can be a or b right?
So if 2 is a then -2 is -a
if 2 is b then -2 is -b
Aren't these mutually exclusive i.e how can we take 2 to be a and -2 to be b?

Also another way I (mistakenly) interpret the statements as if 2 (a or b) is in set then b (or a) can be any nos in the set? for example 5 then we cant get -4


please help!

cheers

------------------
S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.

It doesn't matter what you call the number.
i) States that if a number is in S, then its opposite is also in S. Meaning, if 1 is in S, then -1 is also in S. If -3 is in S, then -(-3) = 3 is also in S.
ii) States that if two numbers are in S, then their product is also in S. Doesn't matter even the two numbers are equal. For example, if 2 is in S, then 2*2 = 4 is also in S. If 2 and -2 are in S, then 2*(-2) = 4 is also in S, 2*4 = 8, -2*4 = -8,...
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Senior Manager
avatar
Joined: 22 Dec 2011
Posts: 298
Followers: 3

Kudos [?]: 185 [0], given: 32

Re: S is a set of integers [#permalink]

Show Tags

New post 12 Oct 2012, 00:47
EvaJager wrote:
(2) says that 2 is in S so this can be a or b right?
So if 2 is a then -2 is -a
if 2 is b then -2 is -b
Aren't these mutually exclusive i.e how can we take 2 to be a and -2 to be b?

Also another way I (mistakenly) interpret the statements as if 2 (a or b) is in set then b (or a) can be any nos in the set? for example 5 then we cant get -4


please help!

cheers

------------------
S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.

It doesn't matter what you call the number.
i) States that if a number is in S, then its opposite is also in S. Meaning, if 1 is in S, then -1 is also in S. If -3 is in S, then -(-3) = 3 is also in S.
ii) States that if two numbers are in S, then their product is also in S. Doesn't matter even the two numbers are equal. For example, if 2 is in S, then 2*2 = 4 is also in S. If 2 and -2 are in S, then 2*(-2) = 4 is also in S, 2*4 = 8, -2*4 = -8,...


ahhh.. I guess i didn't give enf credit to stipulated conditions
It says ii) if EACH of a and b is in S, then ab is in S.

So for ANY A or B in the set then a*b in the set so we definitely know 2 and -2 are in the set hence we are Good.....

thanks for your response EvaJager
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9242
Followers: 454

Kudos [?]: 115 [0], given: 0

Premium Member
Re: S is a set of integers such that i) if a is in S, then –a [#permalink]

Show Tags

New post 26 Dec 2013, 14:58
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5632

Kudos [?]: 68313 [0], given: 9797

Re: S is a set of integers such that i) if a is in S, then –a [#permalink]

Show Tags

New post 27 Dec 2013, 03:37
Expert's post
boomtangboy wrote:
S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is –4 in S?

(1) 1 is in S.
(2) 2 is in S.


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.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 23 Jan 2013
Posts: 173
Concentration: Technology, Other
Schools: Haas
GMAT Date: 01-14-2015
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 37 [0], given: 41

GMAT ToolKit User
Re: S is a set of integers such that i) if a is in S, then –a [#permalink]

Show Tags

New post 24 Jun 2014, 12:19
Bunuel wrote:
S is a set of integers such that i) if a is in S, then –a is in S, and ii) if each of a and b is in S, then ab is in S. Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Answer: B.

Similar questions:
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.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 it helps.




Hi Bunnel ,

I am a little confused with this one .
In stmt A ) i get the elements in the set as 1 and -1 ... i did not find 12 so i thought the Set S has only two elements .. hence We could answer the question that 12 is not present in the set ?

However later on i saw that this is not sufficient to answer the question how can 12 be present in the set with Stmt 1 yields on two values 1 , -1 ?

Thanks and Regards ,
Sheldon Rodrigues
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5632

Kudos [?]: 68313 [0], given: 9797

Re: S is a set of integers such that i) if a is in S, then –a [#permalink]

Show Tags

New post 24 Jun 2014, 12:58
Expert's post
shelrod007 wrote:
Bunuel wrote:
S is a set of integers such that i) if a is in S, then –a is in S, and ii) if each of a and b is in S, then ab is in S. Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Answer: B.

Similar questions:
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.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 it helps.




Hi Bunnel ,

I am a little confused with this one .
In stmt A ) i get the elements in the set as 1 and -1 ... i did not find 12 so i thought the Set S has only two elements .. hence We could answer the question that 12 is not present in the set ?

However later on i saw that this is not sufficient to answer the question how can 12 be present in the set with Stmt 1 yields on two values 1 , -1 ?

Thanks and Regards ,
Sheldon Rodrigues


1 and -1 may NOT be the only numbers in S. S could contain a whole bunch of other numbers. For example, the set could be:
{..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...}
{..., -5, -3, -1, 1, 3, 5, ...}

Hope it's clear.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9242
Followers: 454

Kudos [?]: 115 [0], given: 0

Premium Member
Re: S is a set of integers such that i) if a is in S, then –a [#permalink]

Show Tags

New post 09 Jul 2015, 05:20
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: S is a set of integers such that i) if a is in S, then –a   [#permalink] 09 Jul 2015, 05:20
    Similar topics Author Replies Last post
Similar
Topics:
17 Experts publish their posts in the topic A set of nonnegative integers consists of madimo 9 09 Oct 2012, 08:33
4 Experts publish their posts in the topic S is a set of integers such that I) If x is in S, then –x is conty911 9 25 Apr 2012, 21:58
2 Experts publish their posts in the topic There is a set of consecutive even integers ajit257 7 28 Mar 2011, 19:35
2 Experts publish their posts in the topic S is a set of integers such that i) if a is in S, then a is banksy 5 24 Feb 2011, 14:15
9 Experts publish their posts in the topic Set S consists of 5 consecutive integers, and set T consists nischalb 5 04 Nov 2006, 04:25
Display posts from previous: Sort by

S is a set of integers such that i) if a is in S, then –a

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.