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

It is currently 27 Aug 2016, 19:53
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

If X and Y are sets of integers, X@Y denotes the set of inte

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34457
Followers: 6279

Kudos [?]: 79676 [0], given: 10022

If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

Show Tags

New post 02 Jan 2014, 06:34
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

64% (01:49) correct 36% (01:03) wrong based on 485 sessions

HideShow timer Statistics

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

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6
(B) 16
(C) 22
(D) 30
(E) 174

Problem Solving
Question: 18
Category: Arithmetic Properties of numbers
Page: 64
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:
1. Please provide your solutions to the questions;
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

_________________

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

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34457
Followers: 6279

Kudos [?]: 79676 [0], given: 10022

Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

Show Tags

New post 02 Jan 2014, 06:34
Expert's post
1
This post was
BOOKMARKED
SOLUTION

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6
(B) 16
(C) 22
(D) 30
(E) 174

The number of integers that belong to set X ONLY is 10-6=4;
The number of integers that belong to set Y ONLY is 18-6=12;

The number of integers that belong to set X or set Y, but not both is 4+12=16.

Answer: B.
_________________

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

3 KUDOS received
Manager
Manager
avatar
Joined: 09 Apr 2013
Posts: 152
Location: India
WE: Supply Chain Management (Consulting)
Followers: 1

Kudos [?]: 83 [3] , given: 24

GMAT ToolKit User
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

Show Tags

New post 02 Jan 2014, 11:15
3
This post received
KUDOS
1
This post was
BOOKMARKED
IMO B.

Set X=10
Set Y=18

both X&Y = 6

(Either X or Y or both) = (X) + (Y) - (both X&Y) = 10+18-6 = 22

Now we want a set of integers from either X or Y but not from both X and Y
X@Y = (Either X or Y or both) - (Both X&Y) = 22-6 = 16.
_________________

+1 KUDOS is the best way to say thanks :-)

"Pay attention to every detail"

2 KUDOS received
Current Student
User avatar
Joined: 03 Feb 2013
Posts: 932
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
Followers: 112

Kudos [?]: 722 [2] , given: 546

Reviews Badge
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

Show Tags

New post 02 Jan 2014, 12:24
2
This post received
KUDOS
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6
(B) 16
(C) 22
(D) 30
(E) 174


As per Set theory :
A@B= A + B - 2(A n B), so 10 + 18-2*6 = 16
_________________

Thanks,
Kinjal
Struggling with GMAT ? Experience http://www.gmatify.com/
My Debrief : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267.html#p1449379
My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961
My Linkedin Handle: https://www.linkedin.com/profile/view?id=AAIAAAbtjagB9G1MrEzTRYDRGroXuSmZO0ZhoK0

Please click on Kudos, if you think the post is helpful

1 KUDOS received
Moderator
Moderator
User avatar
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
WE: Business Development (Other)
Followers: 42

Kudos [?]: 615 [1] , given: 723

Premium Member Reviews Badge
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

Show Tags

New post 03 Jan 2014, 00:53
1
This post received
KUDOS
If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6
(B) 16
(C) 22
(D) 30
(E) 174
Attachment:
untitled1.PNG
untitled1.PNG [ 3.39 KiB | Viewed 4718 times ]


Sol: Look at above figure.
Now X@Y = Number of elements in X and Y which are not present in Both.

So X@Y= 10-6+18-6= 16 Ans B
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

1 KUDOS received
Manager
Manager
avatar
Joined: 20 Dec 2013
Posts: 125
Followers: 7

Kudos [?]: 82 [1] , given: 1

Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

Show Tags

New post 03 Jan 2014, 04:03
1
This post received
KUDOS
If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6
(B) 16
(C) 22
(D) 30
(E) 174

Exactly 1 = X + Y - 2(X&Y)

When you add X and Y the intersection gets added twice hence we have to deduct it twice :)

Exactly 1 = 10 + 18 - 12 = 16

Answer B
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34457
Followers: 6279

Kudos [?]: 79676 [0], given: 10022

Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

Show Tags

New post 05 Jan 2014, 11:13
SOLUTION

If X and Y are sets of integers, X@Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X@Y consists of how many integers?

(A) 6
(B) 16
(C) 22
(D) 30
(E) 174

The number of integers that belong to set X ONLY is 10-6=4;
The number of integers that belong to set Y ONLY is 18-6=12;

The number of integers that belong to set X or set Y, but not both is 4+12=16.

Answer: B.
_________________

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

Intern
Intern
avatar
Joined: 03 Aug 2014
Posts: 21
Followers: 0

Kudos [?]: 0 [0], given: 18

Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

Show Tags

New post 28 May 2015, 20:03
Is it possible to solve this problem using a matrix?
Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
Joined: 04 Jan 2015
Posts: 350
Followers: 103

Kudos [?]: 810 [1] , given: 84

Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

Show Tags

New post 29 May 2015, 01:02
1
This post received
KUDOS
Expert's post
cg0588 wrote:
Is it possible to solve this problem using a matrix?


Hi cg0588,

The question asks us the number of integers which belong to set X or Set Y but not both. This would be equal to the number of integers which belong to only set X + number of integers which belong to only set Y

Please find below the matrix diagram of the solution

Image

We are given that set X consists of 10 integers out of which there are 6 integers which are common to set Y. Hence integers which belong to only set X = 10 - 6 = 4

Similarly, we know that set Y consists of 18 integers. As there are 6 integers which are common to set X, we will have 18 - 6 = 12 integers which belong to only set Y.

Thus number of integers which belong to set X or set Y but not both = 4 + 12 = 16

Hope it's clear :)

Regards
Harsh
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11103
Followers: 511

Kudos [?]: 134 [0], given: 0

Premium Member
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

Show Tags

New post 18 Jul 2016, 20:32
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: If X and Y are sets of integers, X@Y denotes the set of inte   [#permalink] 18 Jul 2016, 20:32
    Similar topics Author Replies Last post
Similar
Topics:
8 Experts publish their posts in the topic X and Y are two sets that contain integers as shown the table above. Gnpth 3 25 Feb 2016, 05:12
7 Experts publish their posts in the topic The expression x#y denotes the product of the consecutive multiples of Bunuel 7 24 Apr 2015, 03:10
6 Experts publish their posts in the topic Two integers x and y are chosen without replacement out of the set {1, Bunuel 11 26 Jan 2015, 05:52
15 Experts publish their posts in the topic If X and Y are sets of integers, X # Y denotes the set of carcass 8 29 May 2012, 09:09
14 Experts publish their posts in the topic Set A contains the consecutive integers ranging from x to y, lifeisshort 11 10 Aug 2010, 13:54
Display posts from previous: Sort by

If X and Y are sets of integers, X@Y denotes the set of inte

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.