Difference between revisions of "2007 AMC 8 Problems/Problem 13"
Spoamath321 (talk | contribs) (→Solution) |
|||
Line 36: | Line 36: | ||
- spoamath321 | - spoamath321 | ||
+ | |||
+ | ==Video Solution by WhyMath== | ||
+ | https://youtu.be/3LtGb3KjhoU | ||
+ | |||
+ | ~savannahsolver | ||
==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 21:45, 20 April 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
.
Solution
Let be the number of elements in
and
.
Since the union is the sum of all elements in and
,
and and
have the same number of elements then,
.
The answer is
Solution 2
First find the number of elements in without including the intersection. There are 2007 elements in total, so there are
elements in
and
excluding the intersection (
). There are
elements in set A after dividing
by
. Add the intersection (
) to get
- spoamath321
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.