2007 AMC 8 Problems/Problem 13
Contents
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
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 | ||
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