睡前问数学题--OG13 Data Sufficiency 134

helenchen0413

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

The table above shows the results of a survey of 100 voters who each responed 'favorable' or 'unfavorable' or 'not sure' when asked about their impressions of candidate M and N. What was the number of voters who responded 'favorable' for both candidates?

1) The number of voters who didn't respond 'favorable' for either candidate was 40
2) The number of voters who responed 'unfavorable' for both candidates was 10

看不懂OG解释,脑子晕了，求大牛解释

mutou000

40+30=70， 这70人是vote favorable at least once (其中包括both的). 当40人didn't vote favorable for either candidate. (这句话可以理解为, unfavorable + not sure + 也没有vote both) 100 - 40 = 60 就是 did vote favorable for one candidate only. 60 compare with 70差别就是both 的人数. 70里面包括了"both", 而60里面没包括) 70-60 = 10. 就是vote favorable for both 的人数.

第二个条件, vote两个都没有的的人数是10. 但是里面有两个未知的factors. favorable 跟 unfavorable. 至少要再知道一个才能 求出来.

所以应该选 A

helenchen0413

好像明白一点了,但是还是有点晕， 当40人didn't vote favorable for either candidate. (这句话可以理解为, unfavorable + not sure + 也没有vote both), 这里的也没有vote both 不太理解,而且上面unfavorable的人加起来明显大于40 啊。。。

aassdd654

比如把X当作vote both for favorite， Y当作单独vote M的， Z当作单独vote N的话，
X+Y+Z= 100 - 40(didn't vote favorable for either candidate)
X+Y = 40
X+Z= 30

所以要得出X的值的话，只需要 X+Y+Z - （Y+X）- （Z+X）= 60 - 70 = -X
X=10

画一个两个圆交叉的图比较容易做