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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

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

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Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
02 Jan 2014, 05:34

Expert's post

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.

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 _________________

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Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
02 Jan 2014, 23:53

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 [ 3.39 KiB | Viewed 1067 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.”

Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
03 Jan 2014, 03:03

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 _________________

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Re: If X and Y are sets of integers, X@Y denotes the set of inte [#permalink]
05 Jan 2014, 10:13

Expert's post

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.