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

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

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29 May 2012, 09:09
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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
[Reveal] Spoiler: OA

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Posts: 39725
Re: If X and Y are sets of integers, X # Y denotes the set of [#permalink]

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29 May 2012, 09:39
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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.

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

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29 May 2012, 16:52
thanks bunuel ..........a tricky question to read carefully, but simple in the end.
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Re: If X and Y are sets of integers, X # Y denotes the set of [#permalink]

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31 May 2012, 04:32
This one could be solved with ease if one happens to draw a venn diagram. Significantly reduces the time.
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Re: If X and Y are sets of integers, X # Y denotes the set of [#permalink]

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31 May 2012, 05:03
The catch is to read the question carefully.

The approach by Bunnel is simple ans straight-forward
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Re: If X and Y are sets of integers, X # Y denotes the set of [#permalink]

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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: 39725
Re: If X and Y are sets of integers, X # Y denotes the set of [#permalink]

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

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

Attachments

x.png [ 5.24 KiB | Viewed 2105 times ]

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

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18 Feb 2016, 00:08
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Re: If X and Y are sets of integers, X # Y denotes the set of   [#permalink] 18 Feb 2016, 00:08
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