185. 17987-!-item-!-187;#058&011677
Of the 200 members of a certain association, each member who speaks German also speaks English, and 70 of the members speak only Spanish. If no member speaks all three languages, how many of the members speak two of the three languages?
(1) 60 of the members speak only English.
(2) 20 of the members do not speak any of the three languages.
the key is C,
but I think 2 is sufficient by itself.
according to the question, we are looking for # of students speaking 2 languages: E or G or S. since E includes G, we are actually looking for E or S.
(2)->200-20=180 is E or G or S which is E or S.
What do I miss? Thanks
-- by 会员 shanefeng (2010/1/3 8:29:48)
185. 17987-!-item-!-187;#058&011677
Of the 200 members of a certain association, each member who speaks German also speaks English, and 70 of the members speak only Spanish. If no member speaks all three languages, how many of the members speak two of the three languages?
(1) 60 of the members speak only English.
(2) 20 of the members do not speak any of the three languages.
the key is C,
but I think 2 is sufficient by itself.
according to the question, we are looking for # of students speaking 2 languages: E or G or S. since E includes G, we are actually looking for E or S.
(2)->200-20=180 is E or G or S which is E or S.
What do I miss? Thanks
-- by 会员 shanefeng (2010/1/3 8:29:48)
你可能理解错了问题，问的是所有会讲两种语言的人的总数。也就是两两交集的和，|E and G|+|E and S|+|G and S| = |G or S or E| - |只讲G| - |只讲E| - |只讲S|- |G and E and S|。
由于讲G都会讲E， |只讲G| = 0；没有人同时讲3种语言，|G and E and S|=0；|只讲S|=70。因此，|E and G|+|E and S|+|G and S| = |G or S or E| - |只讲G|。
可见，至少还要2个条件，才能求解。
条件1说明了|只讲E|。条件2说了|E or G or S| = 180。
-- by 会员 大荣 (2010/1/3 12:32:55)
