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An investment firm considers four analysts for annual performance bonuses. Each analyst is evaluated across several metrics and receives a final score out of the same maximum number of points. To qualify for a performance bonus, an analyst must score at least 70% of that maximum. After the evaluations, the four analysts have scores in the ratio 8 : 7 : 6 : 5, and their average score is 65% of the maximum. How many analysts qualify for a performance bonus?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
26 Apr 2026, 11:14
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Official Solution:
An investment firm considers four analysts for annual performance bonuses. Each analyst is evaluated across several metrics and receives a final score out of the same maximum number of points. To qualify for a performance bonus, an analyst must score at least 70% of that maximum. After the evaluations, the four analysts have scores in the ratio 8 : 7 : 6 : 5, and their average score is 65% of the maximum. How many analysts qualify for a performance bonus?
A. 0
B. 1
C. 2
D. 3
E. 4
Let the four scores be \(8k\), \(7k\), \(6k\), and \(5k\).
Their average is:
\(\frac{8k + 7k + 6k + 5k}{4} = \frac{26k}{4} = 6.5k\)
We are told the average equals 65% of the maximum score. So \(6.5k = 65%\) of the maximum. That means \(1k = 10%\) of the maximum.
So the four scores are:
\(8k = 80%\)
\(7k = 70%\)
\(6k = 60%\)
\(5k = 50%\)
An analyst qualifies with at least 70%.
Thus, the analysts scoring 80% and 70% qualify for the bonus.
Answer: C
An investment firm considers four analysts for annual performance bonuses. Each analyst is evaluated across several metrics and receives a final score out of the same maximum number of points. To qualify for a performance bonus, an analyst must score at least 70% of that maximum. After the evaluations, the four analysts have scores in the ratio 8 : 7 : 6 : 5, and their average score is 65% of the maximum. How many analysts qualify for a performance bonus?
A. 0
B. 1
C. 2
D. 3
E. 4
Let the four scores be \(8k\), \(7k\), \(6k\), and \(5k\).
Their average is:
\(\frac{8k + 7k + 6k + 5k}{4} = \frac{26k}{4} = 6.5k\)
We are told the average equals 65% of the maximum score. So \(6.5k = 65%\) of the maximum. That means \(1k = 10%\) of the maximum.
So the four scores are:
\(8k = 80%\)
\(7k = 70%\)
\(6k = 60%\)
\(5k = 50%\)
An analyst qualifies with at least 70%.
Thus, the analysts scoring 80% and 70% qualify for the bonus.
Answer: C
