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.



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".

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.


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

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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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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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

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

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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(1) voters who respond "favorable" for either = 60
Given,
x= Favorable just candidate M
z= Favorable just candidate N
y = favorable both
x + y + z = 60
from the chart:
x + y =40
z + y = 30
Then, y = 10. SUFFICIENT

(2) Insufficient. There are three options. Unfavorable it's just 1 of the three responses of the voters. It doesn't help..

(A)

Hi karishma,

Question for you:
According to statement 1, 40 is the count of folks, who didn't vote favorably for either of the two candidates. This this mean 40 folks were either in Unfavorable, Not Sure Bucket, or Both
According to statement 2, 45 folks are in the Unfavorable bucket alone.

My problem is that I am seeing a contradiction between statement 1 and statement 2. Statement 1 clearly shows that ONLY 40 folks like in the Unfavorable and Not Sure bucket. So how come the Not sure bucket - according to statement 2 - alone is carrying 45 folks?

So, hypothetically speaking, if there were only 2 categories "Favorable" and "Unfavorable" and just for the sake of argument, we combined Unfavorable and Unsure, then wouldn't Statement 2 be sufficient?

200 total votes - 60 (unfavorable for M) - 70 (unfavorable for N) - (10 unfavorable for both) = 60 (who responded "Favorable" for at least 1 candidate?)

Is this logic sound?

Thanks