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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] New post 29 May 2012, 08:09
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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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Re: If X and Y are sets of integers, X # Y denotes the set of [#permalink] New post 29 May 2012, 08:39
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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.

Answer: B.
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Re: If X and Y are sets of integers, X # Y denotes the set of [#permalink] New post 29 May 2012, 15:52
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Re: If X and Y are sets of integers, X # Y denotes the set of [#permalink] New post 31 May 2012, 03:32
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] New post 31 May 2012, 04:03
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] New post 09 Jul 2014, 08:04
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.

Answer: B.


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??
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Re: If X and Y are sets of integers, X # Y denotes the set of [#permalink] New post 09 Jul 2014, 08:16
Expert's post
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.

Answer: B.


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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If X and Y are sets of integers, X # Y denotes the set of [#permalink] New post 10 Jul 2014, 00:44
X #Y represents the shaded region as shown in diagram

Answer = 16 = B
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Re: If X and Y are sets of integers, X # Y denotes the set of   [#permalink] 10 Jul 2014, 00:44
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