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

(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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Hi Bunuel, VeritasKarishma
This cannot be done via Venn diagrams, right?

Thanks!

Such questions are far more suited to 2 by 2 matrices but can be done using venn diagrams too. There are some solutions on page 2 using venn diagrams. Check this:
https://gmatclub.com/forum/the-table-ab ... l#p1767001
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Hi VeritasKarishma,

Thank you for your explanations on this question. Request you to help with the below solution

1) This is my matrix and I am able to solve the question putting 40 (above 70) in this matrix.
For Option 1
However the question is "who did not respond favorable to either" should mean who responded favourable to both or who did not respond favourable to both. My understanding is it should be worded as who did not respond favourable to both.

Not for either A or B = For Both A & B + Not for Both A & B.

So i feel the option is worded wrong ?

Also is the above method correct.

TIA

What you are suggesting is ambiguous.
Does 'not favourable to both' mean 'not favourable to A and not favourable to B' or does it mean 'not favourable to both but could be favourable to one of them'

'not favourable to either' clearly means 'not favourable to A and not favourable to B'

'I don't like either' means I like neither.

I don't understand how you arrived at 10 so unable to say if the method is correct.
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I want to use the basic formula for the overlapping sets.

\(Total = Event \ 1+Event \ 1-Both+Neither\)

Favorable for both candidates \(= X\)

Favorable for both candidates \(N= Y\)

Both \(= B\)

Neither \(= N\)

\(Thus, \)

\(100=X+Y-B+N\)

\(The \ total \ X=40+30=70\), we don't need Y

As we are asked to figure out both for the Favorable condition only so, the equation will be:

\(100=70-B+N\)

(1) \(N= 40\)

\(100=70-B+40\)

\(B=10\) SUFFICIENT.

(2) As we are working on favorable candidates for both the candidates; "Unfavorable" for both candidates = 10 will not be in our in help. Insufficient.

Ans. A\(\)
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