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In a training workshop, each participant took a certification quiz exactly once, either remotely or in person. The average (arithmetic mean) score on the quiz for all participants was 84. What was the average (arithmetic mean) score of the participants who completed the quiz remotely?
(1) There were 30 participants in the workshop.
(2) One sixth of the participants completed the quiz in person, with an average (arithmetic mean) score of 90.
(1) There were 30 participants in the workshop.
(2) One sixth of the participants completed the quiz in person, with an average (arithmetic mean) score of 90.
26 Apr 2026, 13:15
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Official Solution:
In a training workshop, each participant took a certification quiz exactly once, either remotely or in person. The average arithmetic mean score on the quiz for all participants was 84. What was the average arithmetic mean score of the participants who completed the quiz remotely?
Let the total number of participants be \(N\). Then the total of all quiz scores is \(84N\).
(1) There were 30 participants in the workshop.
This gives \(N = 30\). Then the total score is \(84 * 30\), but we still do not know how many participants were remote or what their total score was. Not sufficient.
(2) One sixth of the participants completed the quiz in person, with an average arithmetic mean score of 90.
One sixth were in person, so in person count = \(\frac{N}{6}\). Their average score was 90, so their total score was \(90 * \frac{N}{6} = 15N\).
Remote count = \(N - \frac{N}{6} = \frac{5N}{6}\).
Remote total score = \(84N - 15N = 69N\).
Remote average = \(\frac{69N}{\frac{5N}{6}} = 69 * \frac{6}{5} = 82.8\).
Sufficient.
Answer: B
In a training workshop, each participant took a certification quiz exactly once, either remotely or in person. The average arithmetic mean score on the quiz for all participants was 84. What was the average arithmetic mean score of the participants who completed the quiz remotely?
Let the total number of participants be \(N\). Then the total of all quiz scores is \(84N\).
(1) There were 30 participants in the workshop.
This gives \(N = 30\). Then the total score is \(84 * 30\), but we still do not know how many participants were remote or what their total score was. Not sufficient.
(2) One sixth of the participants completed the quiz in person, with an average arithmetic mean score of 90.
One sixth were in person, so in person count = \(\frac{N}{6}\). Their average score was 90, so their total score was \(90 * \frac{N}{6} = 15N\).
Remote count = \(N - \frac{N}{6} = \frac{5N}{6}\).
Remote total score = \(84N - 15N = 69N\).
Remote average = \(\frac{69N}{\frac{5N}{6}} = 69 * \frac{6}{5} = 82.8\).
Sufficient.
Answer: B
