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

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Intern
Joined: 08 Sep 2005
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If X and Y are sets of integers, X # Y denotes the set of [#permalink]  07 Apr 2006, 19:40
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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

SVP
Joined: 14 Dec 2004
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B) 16

with 6 common integers, X is left with 4 integers & Y is left with 12 integers.

So, X#Y = 16

Is it this simple? Am I trapped?
Manager
Joined: 27 Mar 2006
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Re: PS [#permalink]  07 Apr 2006, 19:49
john2005 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

Since

Total number of elements in X but not X and Y = Total number of elements in X - Total number of elements in X and Y

= 10 - 6 = 4

Total number of elements in Y but not X and Y = Total number of elements in Y - Total number of elements in X and Y

= 18 - 6 = 12

Hence total number of elements in X # Y but not common to X and Y = 4 + 12 = 16

Manager
Joined: 21 Dec 2005
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B sounds more plausible now..

(18-6) + (12-6)=16

What's the OA
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