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

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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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, 23:39
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Expert's post
Venkitaraman wrote:
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

No. It is unfavorable to at least one.

The 10 you subtract is because 10 is double counted.

20 people voted unfavorable for M. This includes 10 people who voted unfavorable for both candidates.
35 people voted unfavorable for N. This also includes 10 people who voted unfavorable for both candidates.
The 10 people are counted twice when we add 20 and 35. So we subtract it out once and we get 45. This includes the people who voted unfavorable for both. Hence "atleast one" is the right term to use here.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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24 Apr 2015, 22:19
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TheNona wrote:
still cannot understand ... any body can present a matrix please ? thanks in advance

For all those who are trying to solve this question with matrix approach.

First, as always make a 3x3 matrix with rows and columns corresponding to mutually exclusive options. Notice that there are 3 unknown values in each row/column. So you need 2 or sum of 2 values in a row/column to find the third/desired value.

Attachment:
File comment: 3x3 matrix

3x3matrix.PNG [ 4.43 KiB | Viewed 2037 times ]

Now, Statement 1 tells you the no. of voters who did not respond favorable for either of the candidates. This means, Not Fav = Unfavorable + Not Sure.
For simplicity, convert the 3x3 matrix to a 2x2 matrix with choices as "Fav" and "Not Fav".
Attachment:
File comment: 2x2 matrix

2x2matrix.PNG [ 3.64 KiB | Viewed 2038 times ]

Now, given the no. of Not Favorable responses = 40, you can easily fill up the rest of the matrix to get to the answer.

Statement 2, gives you only the no. of unfavorable responses = 10. Remember, you need at least 2 sum of 2 other values to find the desired value. You can put it in the 3x3 matrix, to find out that the statement 2 is clearly insufficient.
Attachment:
File comment: 3x3 matrix for statement 2

3x3matrix statement 2.PNG [ 4.47 KiB | Viewed 2038 times ]

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

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16 Jun 2015, 09:06
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.

Hi, I still don't understand, why don't you count "NOT SURE" here ?
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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24 May 2016, 03:18
akhilbajaj wrote:
TheNona wrote:
still cannot understand ... any body can present a matrix please ? thanks in advance

For all those who are trying to solve this question with matrix approach.

First, as always make a 3x3 matrix with rows and columns corresponding to mutually exclusive options. Notice that there are 3 unknown values in each row/column. So you need 2 or sum of 2 values in a row/column to find the third/desired value.

Attachment:
3x3matrix.PNG

Now, Statement 1 tells you the no. of voters who did not respond favorable for either of the candidates. This means, Not Fav = Unfavorable + Not Sure.
For simplicity, convert the 3x3 matrix to a 2x2 matrix with choices as "Fav" and "Not Fav".
Attachment:
2x2matrix.PNG

Now, given the no. of Not Favorable responses = 40, you can easily fill up the rest of the matrix to get to the answer.

Statement 2, gives you only the no. of unfavorable responses = 10. Remember, you need at least 2 sum of 2 other values to find the desired value. You can put it in the 3x3 matrix, to find out that the statement 2 is clearly insufficient.
Attachment:
3x3matrix statement 2.PNG

Hope this helps.

wow man the 3x3 matrix rocks. in fact as noted above we need only colum favorable for solution, all others are just a distraction
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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06 Jul 2016, 05:06
Bunuel wrote:

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.

Why we are not considering the option of "NOT SURE" to vote i.e. 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. -- Over here why 60 = voters who responded either favorable or NOT SURE.

I am sure I am missing something silly but I unable to figure it out. Please help.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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06 Jul 2016, 20:38
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gauraku wrote:
Bunuel wrote:

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.

Why we are not considering the option of "NOT SURE" to vote i.e. 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. -- Over here why 60 = voters who responded either favorable or NOT SURE.

I am sure I am missing something silly but I unable to figure it out. Please help.

40 => People who did not respond "favourable" to either candidate. Then what did they respond? Either "Unfavourable" or "Not sure" to both candidates. 40 is not the number of people who respond "unfavourable". They are the ones who did not respond "favourable".
So 100 - 40 = 60 people responded "favourable" to at least one candidate. To the other candidate, they could have responded with "unfavourable" or "not sure" but to one at least they did respond with "favourable".
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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24 Sep 2016, 03:59
The tricky part with this is to understand that each column of the table maps to a 2 overlap set diagram.

I dont know how easy is to spot this under real GMAT conditions so any hints would be appreciated.
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The table below shows the results of a survey of 100 voters [#permalink]

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23 Nov 2016, 18:25
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Tough one! Attached is a visual (with Venn diagrams) that should help. They key concept being tested here is realizing that the opposite of "neither of" is "at least one of," and that those two categories combine for 100% of the total.
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Screen Shot 2016-11-23 at 6.25.08 PM.png [ 119.81 KiB | Viewed 996 times ]

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

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10 Dec 2016, 13:33
Hope this illustration helps. Experts please confirm.
Attachments

x.PNG [ 35.99 KiB | Viewed 945 times ]

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

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23 Apr 2017, 06:01
Bunuel , IanStewart, VeritasPrepKarishma for statement 1 alone - why is it necessary that out of the 100 voters, the remaining 60 voters necessarily voted "favorable" for M/N or both. Some of them could have merely voted "not sure" or "unfavorable" for both of them but not all of them may have compulsorily voted "favorable" for either one of them. As this is not explicitly mentioned, that was what threw me off while solving the question. Please help
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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24 Apr 2017, 01:28
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Expert's post
Bunuel , IanStewart, VeritasPrepKarishma for statement 1 alone - why is it necessary that out of the 100 voters, the remaining 60 voters necessarily voted "favorable" for M/N or both. Some of them could have merely voted "not sure" or "unfavorable" for both of them but not all of them may have compulsorily voted "favorable" for either one of them. As this is not explicitly mentioned, that was what threw me off while solving the question. Please help

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

Out of 100 people, 40 did not vote favourable for either. They voted either unfavourable or 'not sure' for both. There were exactly 40 such people. So what about the other 60 people? It means the rest of the 60 people gave Favorable to at least one or both the candidates.
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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03 Jul 2017, 15:57
oh, I get it, I fell to the trap of the second.
people who did not respond to "favorable" is different from those who did not respond to "unfavorable".
both of them have nothing to do with each other => A is correct
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The table below shows the results of a survey of 100 voters [#permalink]

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03 Aug 2017, 19:08
Thanks for expert's explanation.

The question's trick in statement ONE is that "do not respond favorable" has included voters who cast "Not sure" and "Unfavorable"

Statement ONE has already gave us the total # of "Not sure" and "Unfavorable", whereas as statement TWO leaves us a mixed votes of "Favorable"(Stat. two gives you unfavorable is 10) AND "Unsure".
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Re: The table below shows the results of a survey of 100 voters [#permalink]

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12 Aug 2017, 05:57
If the question would have given the second statement as

The number of voters who responded "unFavorable" for either candidate was 10?
Would will be the possible scenario in that case?
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Re: The table below shows the results of a survey of 100 voters   [#permalink] 12 Aug 2017, 05:57

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