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A survey of 100 voters

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A survey of 100 voters

by TheAnuja55 » Thu Nov 01, 2012 9:13 am
----------------|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.
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Nov 01, 2012 12:42 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 SwatiAgarwal » Sat Nov 03, 2012 4:30 am
TheAnuja55 wrote:----------------|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.
Make a Venn diagram of Favourable votes where everything else (unfavaourable and not sure) is in neither category)
Image

From question stem we have
Fm + Fn + 2Fmn = 40 + 30 = 70
And the questions asks us to find Fmn

Now consider option 1 alone
it tells us that
Fm + Fn + Fmn = 60
From above we can say Fmn=10.

We narrowed down answer to D and A
Now consider option 2 alone
it tells us that
Um + Un + Umn = 10
This only helps us to know about some part of the people who are in the Neither category of the Venn diagram we made earlier. But it does not tell us anything about the favourable votes.
Option 2 is insufficient and
so the answer is A
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