At a two-candidate election for mayor, 3/4 of the registered voters ca

According to the question stem, 3/4th of the voters cast ballots. Let the total no of voters = x (One thing which might be little confusing here is the use of word "registered". We might assume that voters may be of two types: registered and not registered - this assumption is not correct because common sense says that only people who are registered can vote (unless clearly stated in question otherwise). So here we will go by the common logic and assume that all the voters are registered)
Now the question becomes a simpler one.

Statement 1:

from question stem we know that voters who cast ballots = 3/4x
So, voters who did not cast ballots = 1/4x = 25000 Hence x = 100,000
But this statement does not give any information about the ballots for winning candidates.
Hence INSUFFICIENT

Statement 2:
We can calculate the percentage of voters who cast for winning ballot but we can not find the absolute number. For that we need the number of registered voters.
Hence INSUFFICIENT

Combining statement 1 and 2:
From statement 1, we have that the number of voters and from statement 2, we have the percentage of winning ballots. So, the numbers of registered voters who cast winning ballots = 75,000*55/100.
SUFFICIENT

Answer is C

is this a venn diagram question / double matrix? If it is how would set up the table?

No it is not, because we do not have overlapping sets. We cannot have a voter who cast the ballot for both candidates. It's a simple word problem.

At a two-candidate election for mayor, 3/4 of the registered voters cast ballots. How many registered voters cast ballots for the winning candidate?

3/4 of the registered voters cast ballots and 1/4 of the registered voters did NOT cast ballots.

(1) 25000 registered voters did not cast ballots in the election --> 25,000 registered voters = 1/4 of the registered voters, thus there are total of 4*25,000=100,000 registered voters and 75,000 of them cast ballots. We don;t know how those people voted. Not sufficient.

(2) Of the registered voters who cast ballots, 55 percent cast ballots for the winning candidate. We know only percentage. Not sufficient.

(1)+(2) 0.55*75,000=41,250 registered voters cast ballots for the winning candidate. Sufficient.

Answer: C.

Hope it's clear.
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