THIS QUESTIONS IS WRONG!!!! there can't be 100 voters, there must be 115 voters for the statements to be logical.
It is possible to a gmat question to be wrong? I thought the statements in Data sufficiency must be true in order to answer the question. But in this case, what the statements are saying can't be true:
There are only 100 voters and they can only vote Favorable, Unfavorable or not sure for the 2 candidates.
Let's say X is people who voted favourable for both candidates, Y Unfavorable for both candidates and Z Not sure for Both Candidates.. You can use the chart or a venn diagram, i think the latter is easier to see.
i) The first statement says that there are 40 who did not vote Favorable for either candidate, or 60 people voted Favorable. We can conclude that (70-x)+40=100 => x=10 (10 people voted favourable for both candidates) (this is also the explanation the
GMAT Official guide gives, which is correct)
Only with this statement the question is not rational, why?: In order to have 100 voters and knowing that 40 people voted not favorable, it must be true that all the people who voted unfavorable for at least one plus all the people who voted not sure for at least one must be 40. Using the same equation it would be (55-y)+(75-z)+60=100 (people who voted Unfavorable for at least one) + (People who voted Not Sure for at least one) + (people who voted Favourable for at least one)=100. This equations end up like this: 90=y+z. But this is impossible, because y≤20 and Z≤35. So y+z ≤55, it can't be 90.
Think it this way, at most there are 20 people who voted Unfavorable for both candidates (the are only 20 who voted unfavorable for candidate M and 35 for candidate N, there can't be more than 20 votes for people who voted for both, in a venn diagram you would see the smaller circle entirely inside the bigger circle) If you said 21 people voted unfavorable for both, it means there are at least 21 who voted unfavorable for candidate M, which we know is not true. Happens the same for the voters of "not sure". At most there are 35 who voted not sure for both, because there are only 35 who voted not sure for candidate N and 40 for candidate M. Also, the smallest number of people who voted for each section is the maximum votes between candidate M and N for each option: Favorable, Unfavorable and Not sure is 40, 35 and 40 respectively, so there must be 115 voters, not 100.
ii) The second statement further demonstrate the inconsistency of this question: If there are 10 who voted unfavorable for both candidates (y=10), this means there are 45 people who voted in the "unfavorable section" making it inconsistent with the first statement (40 people did not respond favorable) unless there are -5 people who voted not sure (which is illogical)