Difference between revisions of "2007 AMC 8 Problems/Problem 13"
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== Solution == | == Solution == | ||
| − | Let <math>x</math> be the number of elements in <math>A</math> and <math>B</math>. | + | Let <math>x</math> be the number of elements in <math>A</math> and <math>B</math> which is equal. |
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| + | Then we could form equation | ||
<math>2x-1001 = 2007</math> | <math>2x-1001 = 2007</math> | ||
Revision as of 11:13, 8 July 2021
Problem
Sets 
and 
, shown in the Venn diagram, have the same number of elements.
Their union has 
elements and their intersection has 
elements. Find
the number of elements in .
![[asy] defaultpen(linewidth(0.7)); draw(Circle(origin, 5)); draw(Circle((5,0), 5)); label("$A$", (0,5), N); label("$B$", (5,5), N); label("$1001$", (2.5, -0.5), N);[/asy]](http://latex.artofproblemsolving.com/b/f/d/bfdb09b66054973cff11a173317d646fe1d66de1.png)
Solution
Let 
be the number of elements in and which is equal.
Then we could form equation
.
The answer is 
Video Solution by WhyMath
~savannahsolver
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
