Difference between revisions of "2007 AMC 8 Problems/Problem 13"
(Tag: Rollback) |
(→Video Solution by WhyMath) |
||
| Line 32: | Line 32: | ||
~savannahsolver | ~savannahsolver | ||
| + | |||
| + | https://www.youtube.com/watch?v=6F9x1XBOAeo | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2007|num-b=12|num-a=14}} | {{AMC8 box|year=2007|num-b=12|num-a=14}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 16:47, 5 September 2022
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
https://www.youtube.com/watch?v=6F9x1XBOAeo
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. 
