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

Question

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

(A) 6
(B) 16
(C) 22
(D) 30
(E) 174

Bunuel · Accepted Answer

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

(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.

cssk · Answer

IMO B.

Set X=10
Set Y=18

both X&Y = 6

(Either X or Y or both) = (X) + (Y) - (both X&Y) = 10+18-6 = 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) = 22-6 = 16.

kinjiGC · Answer

As per Set theory :
A@B= A + B - 2(A n B), so 10 + 18-2*6 = 16

WoundedTiger · Answer

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

PerfectScores · Answer

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

Exactly 1 = 10 + 18 - 12 = 16 Answer B

GGMAT760 · Answer

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??

Bunuel · Answer

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.

PareshGmat · Answer

X #Y represents the shaded region as shown in diagram

Answer = 16 = B

cg0588 · Answer

Is it possible to solve this problem using a matrix?

EgmatQuantExpert · Answer

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 https://e-gmat.com/blogs/wp-content/uploads/2015/05/GC-Matrix.jpg 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

ScottTargetTestPrep · Answer

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

CEdward · Answer

Overlapping sets question staring us right in the face.

X = 10
Y = 18
X and Y = 6

10 - 6 = 4
18 - 6 = 12

4 + 12 = 16

B.

sidc07 · Answer

v v v simple solution:

total = 10+18-6;
total=22;

total = exactly 1(ans) +exactly 2;
22= exactly 1 + 6;
exactly 1 = 16;

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

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

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