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Word problem-TRICKY

by \'manpreet singh » Sun Jul 01, 2012 9:22 am
Fav Unfavor Not Sure
Candidate M 40 20 40
Candidate N 30 35 35

Q.1)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.

please explain me the solution i messed up this question(unable to post the table properly ? :? :?: :!: :|
hope you can figure out..
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Source: — Data Sufficiency |
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by Jim@StratusPrep » Sun Jul 01, 2012 10:27 am
Break the 2 groups into Favorable and Not Favorable (this includes unfavorable and not sure) and then M and N.

So if 40 did not respond favorable (or responded unfavorable or not sure) then 60 must have responded favorable.

2) tells us nothing

A is the answer.
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by \'manpreet singh » Sun Jul 01, 2012 1:29 pm
Jim@StratusPrep wrote:Break the 2 groups into Favorable and Not Favorable (this includes unfavorable and not sure) and then M and N.

So if 40 did not respond favorable (or responded unfavorable or not sure) then 60 must have responded favorable.

2) tells us nothing

A is the answer.

BUT HOW DO YOU GET BOTH FAVOURABLE FROM IT....
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by GMATGuruNY » Sun Jul 01, 2012 7:20 pm
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.
Thus, the total number of who responded 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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by \'manpreet singh » Sun Jul 01, 2012 7:34 pm
Thanks Mitch, finally got it cleared.
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