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.
Total Favorable = Favorable for M + Favorable for N - Favorable for Both
The big idea with overlapping group problems is to SUBTRACT THE OVERLAP.
When we count the number who responded Favorable for M and the number who responded Favorable for N, the number who responded Favorable for BOTH -- the OVERLAP -- gets counted twice.
So that we don't double-count the overlap, it must be SUBTRACTED from the total.
Since Favorable for M = 40 and Favorable for N = 30, we get:
Total = 40 + 30 - both
Both = 70 - total.
Question rephrased: What was the TOTAL number who responded Favorable?
Statement 1: The number of voters who did not respond favorable for either candidate was 40.
Since 40 did NOT respond Favorable, the total number who DID respond Favorable = 100-40 = 60.
SUFFICIENT.
Statement 2: The number of voters who responded unfavorable for both candidates was 10.
No way to determine the total number who responded Favorable.
INSUFFICIENT.
The correct answer is
A.
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