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

 It is currently 23 Oct 2019, 08:38

### 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

# 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: 58465
If X and Y are sets of integers, X@Y denotes the set of inte  [#permalink]

### Show Tags

29 May 2012, 09:09
3
19
00:00

Difficulty:

25% (medium)

Question Stats:

68% (01:06) correct 32% (01:07) wrong based on 860 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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58465
If X and Y are sets of integers, X@Y denotes the set of inte  [#permalink]

### Show Tags

02 Jan 2014, 06:34
3
12
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.

_________________
##### General Discussion
Manager
Joined: 09 Apr 2013
Posts: 97
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
2
1
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"
Director
Joined: 03 Feb 2013
Posts: 835
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
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: 660
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
2
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 11247 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: 116
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
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
Intern
Joined: 22 Feb 2014
Posts: 25
Re: If X and Y are sets of integers, X@Y denotes the set of inte  [#permalink]

### Show Tags

09 Jul 2014, 09:04
Bunuel wrote:
carcass wrote:
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.

Hi

I know its silly question but can you please clear my understanding?
Why cannot I do.... 10+18-6??? am I not deducting both from X and Y by doing this??
Math Expert
Joined: 02 Sep 2009
Posts: 58465
Re: If X and Y are sets of integers, X@Y denotes the set of inte  [#permalink]

### Show Tags

09 Jul 2014, 09:16
GGMAT760 wrote:
Bunuel wrote:
carcass wrote:
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.

Hi

I know its silly question but can you please clear my understanding?
Why cannot I do.... 10+18-6??? am I not deducting both from X and Y by doing this??

That way you'll get the total number of elements in X and y, while we need the number of elements that belong to set X or set Y, but not both.

6 elements belong to both X and y, thus there are 10-6=4 unique elements in X and 18-6=12 unique elements in Y. Thus there are total of 4 + 12 = 16 unique elements in X and Y.

Hope it's clear.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If X and Y are sets of integers, X@Y denotes the set of inte  [#permalink]

### Show Tags

10 Jul 2014, 01:44
2
X #Y represents the shaded region as shown in diagram

Attachments

x.png [ 5.24 KiB | Viewed 5857 times ]

_________________
Kindly press "+1 Kudos" to appreciate
Intern
Joined: 03 Aug 2014
Posts: 16
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: 3092
Re: If X and Y are sets of integers, X@Y denotes the set of inte  [#permalink]

### Show Tags

29 May 2015, 01:02
2
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
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8137
Location: United States (CA)
Re: If X and Y are sets of integers, X@Y denotes the set of inte  [#permalink]

### Show Tags

06 Mar 2018, 08:00
Quote:

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

Note that the 6 numbers belonging to both sets must be subtracted from set X and again from set Y.

We can use the equation:

X@Y= set X - both + set Y - both

X@Y = 10 - 6 + 18 - 6 = 16

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Senior Manager
Joined: 26 Jun 2017
Posts: 399
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)
Re: If X and Y are sets of integers, X@Y denotes the set of inte  [#permalink]

### Show Tags

22 Feb 2019, 14:44
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

Problem Solving
Question: 18
Category: Arithmetic Properties of numbers
Page: 64
Difficulty: 600

(10-6) + (20-6) = 16
Re: If X and Y are sets of integers, X@Y denotes the set of inte   [#permalink] 22 Feb 2019, 14:44
Display posts from previous: Sort by