Question 5

Explanation

Our goal is to find the number of votes obtained by O. Let's analyze each statement related to O:

Analysis of Statement 2:

"O received one-fourth of the total votes."

Mathematically, this can be written as:

This statement gives the relationship between O's votes and the Total Votes, but we do not yet know the value of Total Votes.

Analysis of Statement 4:

"There were $480$ votes cast."

This statement provides the exact value for Total Votes:

Conclusion:

By combining Statement 2 and Statement 4, we can calculate O's votes:

Statements 1 and 3 are not needed as they only provide information about the relationships between other candidates' votes (M, N, P) which do not directly affect the calculation of O's absolute vote count without first knowing the total votes.

Therefore, the information needed is 2 and 4.