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.
I wouldn't do much math for this problem. We're looking for the number who voted favorable for both M and N. In other words, the overlap between the 2 favorable groups.
The big idea with overlapping group problems is to
subtract the overlap. When we count the number who voted favorable for M and the number who voted favorable for N, the number who voted favorable for both -- the overlap -- gets counted twice. Thus, so that the overlap doesn't get double-counted, it must be subtracted from the total:
Total favorable = Favorable for M + Favorable for N - Favorable for Both
Since we know that 40 voted favorable for M and that 30 voted favorable for N, to solve for the number who voted favorable for both -- the overlap -- we need to know the total number of favorable votes.
Question rephrased: What was the total number of favorable votes?
Statement 1: The number of voters who did not respond favorable for either candidate was 40.
If 40 did not respond favorable for either candidate, then the total who registered at least one favorable vote = 100-40 = 60.
Sufficient.
To solve:
60 = 40 + 30 - both.
Both = 10.
Statement 2: The number of voters who responded unfavorable for both candidates was 10.
Tells us the overlap between the 2 unfavorable groups. Doesn't help us to determine the overlap between the 2 favorable groups.
Insufficient.
The correct answer is
A.
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