GMAT
题目
A box contains white marbles and black marbles, all identical except for color. If one marble is drawn at random, the probability that it is a white marble is . Six white marbles are added to the box, but no black marbles are added. Now, if one marble is drawn at random, the probability that it is a white marble is .
Quantity A
Quantity B
解析
盒中最少有8颗弹珠（其中7颗为白色）。若增加6颗弹珠，则有13颗白色弹珠，总数为14颗，此时新概率为13/14 < 14/15。一般情况下，初始时有7N颗白色弹珠和8N颗弹珠，加入6颗白色弹珠后，概率变为(7N+6)/(8N+6)。为证明该一般情况，令(7N+6)/(8N+6) < 14/15，则：
(7N+6)×15 < (8N+6)×14
105N + 90 < 112N + 84
-7N < -6
N > 6/7
由于N为正整数，上式恒成立。因此正确答案为B。
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