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Sets problem

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Sets problem [#permalink]

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New post 07 Sep 2009, 17:04
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Please, explain your answer. Thank you,
----------------------------------------
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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Re: Sets problem [#permalink]

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New post 07 Sep 2009, 22:33
I did this for the OG, but haven't checked the answer yet. So this for now is just my answer. I tried my best to line them all up.

I got A.

FN NFN NSN TN
FM 40
NFM 20
NSM 40
TM 30 35 35

F=Favorable NF= Not favorable NS= Not sure T=Total

Statement one gives you this

FN NFN NSN TN
FM Z 40
NFM Y X X 20
NSM Y X X 40
TM 30 35 35

The area with the Xs equals 40. We see that the area with the Xs + the area with the Ys=60 (note: 20+40 under TN). Therefore the Ys equals 20. Then you take TM-20=Z. TM=30-20=10 for Z. Z is Favorable for both. So 1 is sufficient.

So statement 2

FN NFN NSN TN
FM 40
NFM 10 20
NSM 40
TM 30 35 35

All you get is 10 in the middle there. You don't have enough information to fill in the rest because there are at least 2 unknowns across the board. So IMO 2 is insufficient.

So my answer is A.
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Re: Sets problem [#permalink]

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New post 07 Sep 2009, 22:42
Wow that looks awful. Didn't line up the way I wanted, but anyway. Maybe it'll be easier to just write out, what I mean.

Statement 1: All of the Non-favorables and Not-Sures for N who were also non-favorable and not sure for M equals to 40. That means because all of the non-favorables and not sures for M equals to 60, ones that voted Not favorable and nots sure for M and Favorable for N equals 20 (works if you do it the other way, but it'll be 70-40=30). All of the Favorables for N equals to 30. Then 30-20 (20 that that are also not favorable and not sure for M) equals to 10, which leaves the favorable M and N. That's your answer.

Statement 2: I believe is insufficient, because you get one number (10), and there are at least 2 variables and that number (10) that make up the total. You need only 1 variable and 2 numbers at least somewhere.

So my answer is A.

Last edited by GmatNY86 on 08 Sep 2009, 21:10, edited 1 time in total.
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Re: Sets problem [#permalink]

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New post 08 Sep 2009, 09:39
Voters responded favorable for at least one candidates =40+30-x=70-x (x responded favorable for both)

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

Answer A.
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Re: Sets problem [#permalink]

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New post 09 Sep 2009, 14:41
Thank you for the explanation! OA is indeed A!
Re: Sets problem   [#permalink] 09 Sep 2009, 14:41
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