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# The table below shows the results of a survey of 100 voters

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The table below shows the results of a survey of 100 voters [#permalink]

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14 Jan 2010, 11:15
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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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Re: What is the result [#permalink]

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14 Jan 2010, 15:03
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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?

Voters responded favorable for at least one candidates = 40+30-x = 70-x (x represent the # of voters who responded favorable for both candidates)

(1) The number of voters who did not respond “favorable” for either candidate was 40 --> The voters responded favorable for at least one 100-40=60=70-x --> x=10. Sufficient.

(2) The number of voters who responded “unfavorable” for both candidates was 10. Clearly not sufficient.

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The table above shows the results of a survey of 100 voters [#permalink]

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03 Jul 2011, 02:20
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How to solve this using 3X3 matrix? and how to solve this using venn diagram formula (M or N) = (M )+ (N )- (M and N)...please explain in detail??? Also, what does statement 1 mean ??and how can it be represented in 3x3 matrix?
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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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Re: The table above shows the results of a survey of 100 voters [#permalink]

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03 Jul 2011, 04:16
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siddhans wrote:
How to solve this using 3X3 matrix? and how to solve this using venn diagram formula (M or N) = (M )+ (N )- (M and N)...please explain in detail??? Also, what does statement 1 mean ??and how can it be represented in 3x3 matrix?
Attachment:
img.doc

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.

A.
No of voters who dint respond favourable = 40
this mean people who responded favourable are 100-40 = 60
therefore No. of people who responded fav for both are 40+30-60 = 10

B not sufficient.
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Re: The table above shows the results of a survey of 100 voters [#permalink]

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03 Jul 2011, 04:17
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siddhans wrote:

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.

A lot of the information in the table just serves as a distraction here. The first column of the table gives us a standard 2-circle Venn diagram: those people who like M, those people who like N, and those people who like both. We want to know how many like both. If we know exactly how many people are in our diagram (i.e. how many people responded 'favourable' to at least one candidate), we can answer that question. Statement 1 tells us that 40 of the 100 people are *not* in our diagram, so 60 people must be in the diagram, and that info is sufficient. I can't draw a Venn diagram here, but I'd fill it in as follows:

Favorable for M only: 40 - x
Favorable for both M and N: x
Favorable for N only: 30 - x

From Statement 1 I know these three quantities add to 60, which gives me one equation in one unknown.

Statement 2 doesn't tell you how many people are in the diagram, so is not sufficient.

As for your question about using a 'matrix' or 'formula' here, I wouldn't consider doing either.
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Re: What is the result [#permalink]

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20 Aug 2011, 12:30
I had trouble to understand this table, bc it says that they asked 100 people, but we have 200 answers.

Can someone please explain me that?

thanks.
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Re: What is the result [#permalink]

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20 Aug 2011, 18:25
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we are seeing 200 responses because each voter casted two votes , one for each candidate.

i.e 1 voter - 2 votes

1. Sufficient

NF+NS = 40

F = 100 - 40 = 60

Assume this F as big overlapping set and now look at the each individual values of this set from the table.

i.e 40+30 - both = F total = 60

=> both = 10

2. not sufficient

because we only know about NF. we dont know anything about the NS and hence we cannot calculate both with the given info.

144144 wrote:
I had trouble to understand this table, bc it says that they asked 100 people, but we have 200 answers.

Can someone please explain me that?

thanks.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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13 Nov 2011, 02:27
Can someone please explain why (1) is sufficient? What I don't understand is this:

We know that 100 people took a survey. From the statement "The number of voters who did not respond “Favorable” for either candidate was 40" we can conclude that 100-40=60 people responded either favorable for at least one or responded unsure. Where am I going wrong?

Thanks a lot.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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13 Nov 2011, 02:52
OK. I solved my previous question. But there's one more:

(1) 40+30=70 is the number of people who responded favorable for at least one candidate.
(2) 70-x is the number of people who responded favorable for exactly one candidate.
(3) 100-40=60 is the number of people who responded favorable for at least one candidate.

What I don't understand is that in (1) we got 70, and in (2) we got 60 for the number of people who responded favorable for at least one candidate. The solution by Bunuel would make sense if 60 was the number of people who responded favorable for exactly one candidate.

I would appreciate if someone could explain.

Thanks a lot.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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13 Nov 2011, 04:31
I think I got it figured out. In 30+40 we have counted the intersection (M&&N) twice.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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21 Mar 2013, 15:25
still cannot understand ... any body can present a matrix please ? thanks in advance
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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22 Mar 2013, 01:12
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TheNona wrote:
still cannot understand ... any body can present a matrix please ? thanks in advance

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.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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22 Mar 2013, 06:03
VeritasPrepKarishma wrote:
TheNona wrote:
still cannot understand ... any body can present a matrix please ? thanks in advance

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.

Thanks Karishma for the great explanation . In fact what I was struggling with is the insufficiency of B . Cannot understand why ?
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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22 Mar 2013, 20:09
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TheNona wrote:
Thanks Karishma for the great explanation . In fact what I was struggling with is the insufficiency of B . Cannot understand why ?

Let's consider statement 2:

(2) The number of voters who responded “unfavorable” for both candidates was 10.

So this means that 90 people replied "favorable" or "not sure" to at least one of the candidates.

Also, going back to the table in the question,
Unfavorable for candidate M = 20
Unfavorable for candidate N = 35
Unfavorable for both = 10
Unfavorable for at least one = 20 + 35 - 10 = 45

So, all we know from here is the following:
1. 10 people responded "unfavorable" to both candidates
2. 35 (= 45 - 10) people responded "unfavorable to one candidate and "favorable" or "not sure" to the other.
3. 55 people responded with "favorable" or "not sure" to both the candidates.

Now we don't know the split between "favorable" and "not sure".
It is possible that 10 people responded "favorable" to both and it is also possible that that number is 15.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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24 Mar 2014, 12:48
I didn't see this explicitly mentioned on this thread or the OA but....

For Statement 1, is this the formula that was used??

A + B - both + neither = total

40 + 30 - X + 40 = 100

X = 10

If so, I'm confused why the total is 100 and not 70, any help would be greatly appreciated thanks!
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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24 Mar 2014, 19:55
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kaji wrote:
I didn't see this explicitly mentioned on this thread or the OA but....

For Statement 1, is this the formula that was used??

A + B - both + neither = total

40 + 30 - X + 40 = 100

X = 10

If so, I'm confused why the total is 100 and not 70, any help would be greatly appreciated thanks!

When you are considering the set of 'neither', you must take the total 'total'.

'total' would be either 60 or 100 (and not 70 because 70 is not the number of people. It is the number of instances which includes double counting of people who favor both candidates) depending on whether you include neither or not.

A + B - Both = 60 (the total number of people who favor at least one)
30 + 40 - Both = 60
Both = 10

OR

A + B - Both + Neither = 100 (total number of people including those who favored neither candidate)
30 + 40 - Both + 40 = 100
Both = 10

Remember, in this formula, 'total' is the total number of people without any double counting.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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11 Aug 2014, 01:07
VeritasPrepKarishma wrote:
TheNona wrote:
Thanks Karishma for the great explanation . In fact what I was struggling with is the insufficiency of B . Cannot understand why ?

Let's consider statement 2:

(2) The number of voters who responded “unfavorable” for both candidates was 10.

So this means that 90 people replied "favorable" or "not sure" to at least one of the candidates.

Also, going back to the table in the question,
Unfavorable for candidate M = 20
Unfavorable for candidate N = 35
Unfavorable for both = 10
Unfavorable for at least one = 20 + 35 - 10 = 45

So, all we know from here is the following:
1. 10 people responded "unfavorable" to both candidates
2. 35 (= 45 - 10) people responded "unfavorable to one candidate and "favorable" or "not sure" to the other.
3. 55 people responded with "favorable" or "not sure" to both the candidates.

Now we don't know the split between "favorable" and "not sure".
It is possible that 10 people responded "favorable" to both and it is also possible that that number is 15.

I don't understand why we assume that the 90 responded "favorable" or "not sure" but concerning the first statement we say that 60 people responded "favorable" ? What about the fraction of the 60 people who responded "not sure"? Are the "not sure" people included in the 40?
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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11 Aug 2014, 21:31
lou34 wrote:
I don't understand why we assume that the 90 responded "favorable" or "not sure" but concerning the first statement we say that 60 people responded "favorable" ? What about the fraction of the 60 people who responded "not sure"? Are the "not sure" people included in the 40?

The structure of the two statements is quite different:

(1) The number of voters who did not respond "Favorable" for either candidate was 40.

40 people did not give "Favorable" to either. It means the rest of the 60 people gave Favorable to at least one or both the candidates.

(2) The number of voters who responded "Unfavorable" for both candidates was 10.

10 people responded Unfavorable for both. It means the rest of the 90 people gave either "Favorable" or "Not Sure" to at least one of the two candidates.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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11 Aug 2014, 23:41
VeritasPrepKarishma wrote:
lou34 wrote:
I don't understand why we assume that the 90 responded "favorable" or "not sure" but concerning the first statement we say that 60 people responded "favorable" ? What about the fraction of the 60 people who responded "not sure"? Are the "not sure" people included in the 40?

The structure of the two statements is quite different:

(1) The number of voters who did not respond "Favorable" for either candidate was 40.

40 people did not give "Favorable" to either. It means the rest of the 60 people gave Favorable to at least one or both the candidates.

(2) The number of voters who responded "Unfavorable" for both candidates was 10.

10 people responded Unfavorable for both. It means the rest of the 90 people gave either "Favorable" or "Not Sure" to at least one of the two candidates.

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Re: The table below shows the results of a survey of 100 voters [#permalink]

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21 Oct 2014, 08:25
Hi Karishma,

Thanks for the detailed explanation. In your response, 'Unfavorable for at least one = 20 + 35 - 10 = 45'. Shouldn't it be "exactly one" instead of "atleast one"

Thanks,
Venkitaraman.S

VeritasPrepKarishma wrote:
TheNona wrote:
Thanks Karishma for the great explanation . In fact what I was struggling with is the insufficiency of B . Cannot understand why ?

Let's consider statement 2:

(2) The number of voters who responded “unfavorable” for both candidates was 10.

So this means that 90 people replied "favorable" or "not sure" to at least one of the candidates.

Also, going back to the table in the question,
Unfavorable for candidate M = 20
Unfavorable for candidate N = 35
Unfavorable for both = 10
Unfavorable for at least one = 20 + 35 - 10 = 45

So, all we know from here is the following:
1. 10 people responded "unfavorable" to both candidates
2. 35 (= 45 - 10) people responded "unfavorable to one candidate and "favorable" or "not sure" to the other.
3. 55 people responded with "favorable" or "not sure" to both the candidates.

Now we don't know the split between "favorable" and "not sure".
It is possible that 10 people responded "favorable" to both and it is also possible that that number is 15.
Re: The table below shows the results of a survey of 100 voters   [#permalink] 21 Oct 2014, 08:25

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