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
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 EditionIf 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




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
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 106=4; The number of integers that belong to set Y ONLY is 186=12; The number of integers that belong to set X or set Y, but not both is 4+12=16. Answer: B.
_________________




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
IMO B. Set X=10 Set Y=18 both X&Y = 6 (Either X or Y or both) = (X) + (Y)  (both X&Y) = 10+186 = 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) = 226 = 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
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
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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 + 182*6 = 16
_________________



Director
Joined: 25 Apr 2012
Posts: 660
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If X and Y are sets of integers, X@Y denotes the set of inte
[#permalink]
Show Tags
03 Jan 2014, 00:53
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= 106+186= 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
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
_________________
76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views
Perfect Scores http://perfectscores.org http://www.youtube.com/perfectscores



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 106=4; The number of integers that belong to set Y ONLY is 186=12; The number of integers that belong to set X or set Y, but not both is 4+12=16. Answer: B. Hi I know its silly question but can you please clear my understanding? Why cannot I do.... 10+186??? 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 106=4; The number of integers that belong to set Y ONLY is 186=12; The number of integers that belong to set X or set Y, but not both is 4+12=16. Answer: B. Hi I know its silly question but can you please clear my understanding? Why cannot I do.... 10+186??? 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 106=4 unique elements in X and 186=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
X #Y represents the shaded region as shown in diagram Answer = 16 = B
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?



eGMAT 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
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 Answer: B
_________________
5star 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 EditionIf 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 (106) + (206) = 16




Re: If X and Y are sets of integers, X@Y denotes the set of inte
[#permalink]
22 Feb 2019, 14:44






