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14 Jan 2010, 12:15
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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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14 Jan 2010, 16:03
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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?
The number of voters who responded favorably to at least one candidate is equal to M + N - Both = 40 + 30 - x = 70 - x (where x represents 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:
Since out of 100 voters 40 did NOT respond “favorable” for either candidate, the remaining 60 voters must have responded favorable for at least one candidate. Hence, 70 - x = 60, which gives x = 10.
Sufficient.
(2) The number of voters who responded “unfavorable” for both candidates was 10.
The above implies that there are 90 people who responded “favorable” for either one or "not sure" for either one. Clearly not sufficient to fin the number of voters who responded favorable for both candidates.
Answer A.
TheNona
I am assuming you are unable to figure out why statement 1 is sufficient. Think of it this way:
(1) The number of voters who did not respond "Favorable" for either candidate was 40.
This means that 60 voters responded 'Favorable' for at least one candidate, right? Now we need to find how many responded Favorable to both.
Now forget this question and think of another sets question:
There are 60 voters in a constituency. Each voter has to vote 'favorable' for at least one of the two candidates - M and N. Candidate M gets 40 favorable votes and candidate N gets 30 favorable votes. How many voters voted 'favorable' for both the candidates?
It's an easy enough question with 2 sets. You will just use
60 = 30 + 40 - Both
Both = 10
This is exactly what is required of you in this question. Just that there is a lot of other data to distract you. You know that 60 voters voted favorable for atleast one candidate. You also know that M got 40 favorable votes and N got 30 favorable votes (from the table int he question). you just need to find the value of 'both'. Focus on what you have to find, and the given relevant info.
Check out the video discussing Overlapping Sets here: https://youtu.be/HRnuURqGhmg
