Spokesperson: In the 2006 election of the city mayor

[MBA Applicant 2007/8]

Spokesperson: In the 2006 election of the city mayor, 55% of the voters were female. All the voters were between ages 18 and 70 and 2/3 of them supported the incumbent mayor. The incumbent mayor won the election with a substantially greater number of votes than any other candidate.

If the statements made by the Spokesperson are true, then which of the following must be true?
A) At least 1/2 of the female voters supported the incumbent mayor.
B) The incumbent mayor received stronger support from the female voters than from the male voters.
C) There were no other candidates in the election who received more than 30% of all the votes.
D) 45% of the voters in the election were male and none of them were 75 years old.
E) If the proportion of male and female voters in the city remains the same, the incumbent mayor is also likely to win the next election.

Can you please help with the appropriate DIAGRAM and explanation as to how you arrived at the correct answer?

[dbernst]

By the phrasing of the question, this problem can be identified as an inference/draw a conclusion critical reasoning argument. Normally, this type of argument does not contain a conclusion. Instead the "argument" will simply be a series of facts. The correct answer of an inference or draw a conclusion argument must be DIRECTLY SUPPORTED BY EVIDENCE FROM THE TEXT. Often, to test whether I have chosen the correct answer, I add the words "It is true that..." before each answer choice. This permits me to accurately assess whether the choice is fully supported by the text.

In the text at hand we are provided with the following facts about the 2006 mayoral election:

1. 55% female voters (so 45% male voters)
2. All voters between 18 and 70
3. 2/3 voted for the incumbent mayor (1/3 voted for other/others)

Now, let's look at the answer choices:

A) At least 1/2 of the female voters supported the incumbent mayor.
- Not necessarily true (for example, let's assume 100 voters. If the incumbent recieved all of the male votes, or 45 votes, than only 22 of 55 female voters would be enough for the incumbent to reach 2/3 of the overall vote total)
B) The incumbent mayor received stronger support from the female voters than from the male voters.
- Same problem as A: Could be true, but not necessarily true
C) There were no other candidates in the election who received more than 30% of all the votes.
-Since the incumbent received 2/3 of the vote, a second candidate could have received up to 1/3 of the vote
D) 45% of the voters in the election were male and none of them were 75 years old.
CORRECT: Facts #1 and #2 directly support this answer choice!
E) If the proportion of male and female voters in the city remains the same, the incumbent mayor is also likely to win the next election.
-Too predictive and way out of scope. We have no idea what will take place in the future.

-dan

Spokesperson: In the 2006 election of the city mayor, 55% of the voters were female. All the voters were between ages 18 and 70 and 2/3 of them supported the incumbent mayor. The incumbent mayor won the election with a substantially greater number of votes than any other candidate.

If the statements made by the Spokesperson are true, then which of the following must be true?

A) At least 1/2 of the female voters supported the incumbent mayor.
B) The incumbent mayor received stronger support from the female voters than from the male voters.
C) There were no other candidates in the election who received more than 30% of all the votes.
D) 45% of the voters in the election were male and none of them were 75 years old.
E) If the proportion of male and female voters in the city remains the same, the incumbent mayor is also likely to win the next election.

Can you please help with the appropriate DIAGRAM and explanation as to how you arrived at the correct answer?