AMC 8 2007 Problem 13
AMC8 2007 年第 13 题
基本计数原理★★★☆☆
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.
如下图所示的文氏图中，集合 A 和集合 B 中的元素个数相等。它们的并集有 2007 个元素，且它们的交集有 1001 个元素。那么求集合 A 中的元素个数。
- A.503
- B.1006
- C.1504
- D.1507
- E.1510
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Let be the number of elements in and which is equal. Then we could form equation 2x-1001 = 20072x = 3008x = 1504. The answer is 1504
Let be the number of elements in not including the intersection. 2007-1001=1006 total elements excluding the intersection. Since we know that A=B, we can find that . Now we need to add the intersection. 503+1001=1504.
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