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If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
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02 Jan 2014, 06:34
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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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach 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!
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Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
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02 Jan 2014, 06:34



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Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
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02 Jan 2014, 11:15
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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.
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Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
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02 Jan 2014, 12:24
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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
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Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
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03 Jan 2014, 00:53
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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 7358 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
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Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
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03 Jan 2014, 04:03
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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
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Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
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05 Jan 2014, 11:13



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



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



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