It is currently 27 Jun 2017, 11:05

### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 39723
If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

02 Jan 2014, 06:34
1
KUDOS
Expert's post
6
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

64% (01:49) correct 36% (01:01) wrong based on 653 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:
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: 39723
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

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.

_________________
Manager
Joined: 09 Apr 2013
Posts: 148
Location: India
WE: Supply Chain Management (Consulting)
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

02 Jan 2014, 11:15
3
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"

Current Student
Joined: 03 Feb 2013
Posts: 941
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

02 Jan 2014, 12:24
2
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

My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961

Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

03 Jan 2014, 00:53
1
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 [ 3.39 KiB | Viewed 6112 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.”

Manager
Joined: 20 Dec 2013
Posts: 132
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

03 Jan 2014, 04:03
1
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

_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org

Math Expert
Joined: 02 Sep 2009
Posts: 39723
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

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.

_________________
Intern
Joined: 03 Aug 2014
Posts: 20
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

28 May 2015, 20:03
Is it possible to solve this problem using a matrix?
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 726
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

29 May 2015, 01:02
1
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

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
Joined: 09 Sep 2013
Posts: 16004
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

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.
_________________
Intern
Joined: 24 Sep 2016
Posts: 42
Location: United States (CT)
GPA: 3.81
WE: Analyst (Venture Capital)
Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]

### Show Tags

02 Feb 2017, 16:52
Its a very simple yet tricky concept to understand. Think of it as a set for example
X = 1,2,3,4,5,6,7,8,9,10
5,6,7,8,9,10
Y=5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,28

Essentially the set of six numbers is being double counted....... so you can add X and Y and than subtract 2*(the set of shared integers which in this case is 6)
Leaving you with 16. Hope this makes it clear.
KUDOS +1 if you like my explanation
Re: If X and Y are sets of integers, X@Y denotes the set of inte   [#permalink] 02 Feb 2017, 16:52
Similar topics Replies Last post
Similar
Topics:
9 The expression x#y denotes the product of the consecutive multiples of 7 06 May 2016, 13:49
11 Two integers x and y are chosen without replacement out of the set {1, 12 06 May 2017, 05:40
16 If X and Y are sets of integers, X # Y denotes the set of 8 18 Feb 2016, 00:08
19 Set T consists of all points (x,y) such that x^2+y^2 =1 13 08 Jul 2015, 22:50
20 Set A contains the consecutive integers ranging from x to y, 12 17 Oct 2016, 05:51
Display posts from previous: Sort by