两人参加竞赛,甲做错了总数的1/3,乙做错了6道题,两人都做错了总数的1/5,两人都做对的题有多少道?( )A. 5 B. 6 C. 7 D. 8

作者: tihaiku 人气: - 评论: 0
问题 两人参加竞赛,甲做错了总数的1/3,乙做错了6道题,两人都做错了总数的1/5,两人都做对的题有多少道?( )
选项 A. 5 B. 6 C. 7 D. 8
答案 C
解析 设总题量为x道,则甲做错了x/3道题,甲乙都答错了x/5道题。再设甲乙都答对的题为y道。将这些数字代入到两集合容斥公式中,可得因为都做对的题目数为整数,则13x/15为整数,那么x必须是15的整数倍。当x=15时,解得y=7,故选C。

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