If a simple majority of the votes cast is required for the proposal to be adopted, which of the following statements, if true, would enable you to determine whether the proposal was adopted?

a. There are more seniors than freshmen on the council.
b. A majority of the freshmen and a majority of the sophomores voted for the proposal.
c. There are 18 seniors on the council.
d. There are the same number of seniors and freshmen combined as there are sophomores and juniors combined.
e. There are more juniors than sophomores and freshmen combined, and more than 90% of the juniors voted against the proposal.

Option C is correct

There are 18 seniors on the council.

Explanation:

The facts we know

- There are 39 council members.

- A proposal was voted for.

- All of the seniors voted for it.

Every single senior present, voted for the proposal.

- None of the freshmen voted for it.

- Some of the juniors and some of the sophomores voted for the proposal and some voted against it; meaning that, at least one junior voted for the proposal, at least one sophomore voted for the proposal, at least one junior voted against the proposal and at least one sophomore voted against the proposal.

- Majority of the 39 votes is required for the proposal to pass; majority of 39 starts from 20.

So we require a minimum of 20 votes to pass the proposal.

So, to the answer now, if 18 seniors are indeed present, that means we automatically have 18 votes for the proposal already (because it is stated that all the seniors voted for the proposal), add that to the at least one junior and at least one sophomore that voted for the proposal and we obtain at least 20 votes that way (which is already the majority).

So, this piece of information (that there are 18 seniors on the council) is enough to tell us that we obtained the majority of votes required to pass the proposal.

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