求解一到数学题，一直搞不明白这类题

andykitch

Q33:

	Favorable	Unfavorable	Not Sure
Candidate M	40	20	40
Candidate N	30	35	35

The table above shows the results of a survey of 100 voters each responded “favorable” or “unfavorable” or “not sure” when asked about their impressions of candidate M and of candidate N.What was the number of voters who responded “favorable” for both candidates?
(1)The number of voters who did not respond “favorable” for either candidate was 40.
(2)The number of voters who responded “unfavorable” for both candidates was 10.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

2010

逐条分析，看看能推出什么结论。别看一堆东东自己吓到了。
（1）说，did not respond “favorable”有40个，那么 respond “favorable”（不管是投一个，还是两个都投）有100-40=60个，再结合表中信息Favorable M的有40个，Favorable N的有30个， 就可以推出 两个都同时 respond “favorable”的有 （30+40）-60=10个。充分了。
（2）同理，responded “unfavorable” for both candidates was 10，那么 not responded “unfavorable” 有100-10=90个。包含Favorable和Not Sure两大类情况，要确定the number of voters who responded “favorable” for both candidates 至少需要信息排除Not Sure的情况，或者如（1）确定Favorable的情况。不充分。

andykitch

谢谢啦。