Data Sufficiency

The table above shows the results of a survey of 100 voters who 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 resunded "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.

Great question. The table isn't helpful by itself, but if we think of each column as a a system of two overlapping groups, we can solve by using Venn diagrams, the groups formula (total = group1 +group2 + neither - both) or the groups table (aka matrix).

The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).



-Patrick

LulaBrazilia wrote:

The table above shows the results of a survey of 100 voters who 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 resunded "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.