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by tonebeeze » Sun Dec 26, 2010 2:04 pm
What is the best approach to solve this advanced overlapping set problem?

124:
Candidate M (40) Favorable (20) Unfavorable (40) Not Sure
Candidate N (30) Favorable (35) Unfavorable (35) Not Sure

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 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.
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Source: — Data Sufficiency |
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by anshumishra » Sun Dec 26, 2010 2:43 pm
tonebeeze wrote:What is the best approach to solve this advanced overlapping set problem?

124:
Candidate M (40) Favorable (20) Unfavorable (40) Not Sure
Candidate N (30) Favorable (35) Unfavorable (35) Not Sure

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 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.
FM -> People who voted favorable to M
FN -> People who voted favorable to N

FM # FN = ? (Note : # -> is intersection)

Statement 1:

The number of voters who did not respond "favorable" for either candidate was 40 => The number of voters who voted favorable for at least on candidate = 100-40 = 60
or
FM U FN = 60 (U -> union)
=> FM U FN = FM + FN - (FM # FN)
=> (FM # FN ) = 40+30-60 = 10 -> Sufficient

Statement 2 :
The number of voters who responded unfavorable for both candidates = 10
- There are two groups which can be affected based on the fact ( not sure and favorable), Hence the data is - Insufficient.

Answer is A.
Thanks
Anshu

(Every mistake is a lesson learned )
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