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Difference between revisions of "2007 AMC 8 Problems/Problem 13"

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The answer is <math>\boxed{C}</math>
 
The answer is <math>\boxed{C}</math>
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==See Also==
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{{AMC8 box|year=2007|num-b=12|num-a=14}}

Revision as of 22:41, 12 November 2012

Problem

Sets $A$ and $B$, shown in the Venn diagram, have the same number of elements. Their union has $2007$ elements and their intersection has $1001$ elements. Find the number of elements in $A$.

AMC8 2007 13.png

$\mathrm{(A)}\ 503 \qquad \mathrm{(B)}\ 1006 \qquad \mathrm{(C)}\ 1504 \qquad \mathrm{(D)}\ 1507 \qquad \mathrm{(E)}\ 1510$

Solution

Let $x$ be the number of elements in $A$ and $B$.

Since the union is the sum of all elements in $A$ and $B$,

and $A$ and $B$ have the same number of elements then,

$2x-1001 = 2007$

$2x = 3008$

$x = 1504$.

The answer is $\boxed{C}$

See Also

2007 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 12 		Followed by
Problem 14
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions
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