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03 Mar 2026, 04:09
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B
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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.
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11 Mar 2026, 01:15
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GMAT Club 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 = N/6. Their average score was 90, so their total score was 90 * N/6 = 15N.
Remote count = N - N/6 = 5N/6.
Remote total score = 84N - 15N = 69N.
Remote average = (69N)/(5N/6) = 69 * 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 = N/6. Their average score was 90, so their total score was 90 * N/6 = 15N.
Remote count = N - N/6 = 5N/6.
Remote total score = 84N - 15N = 69N.
Remote average = (69N)/(5N/6) = 69 * 6/5 = 82.8.
Sufficient.
Answer: B.
General Discussion
03 Mar 2026, 06:21
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Given, let p= mean score of people gave test in person, r= mean score of people gave remotely
n= number of people who have given test in person, m= number of people who have given test remotely
we know, (np+mr)/(m+n) = 84, to find: r?
Sol.
Statement 1-> m+n = 30
Here value of m, n can be anything, neither do we know the value or p, thus it is insufficient, cancel option A and D
Statement 2-> n=(m+n)/6, and p = 90, lets take m+n=N
Now, equation becomes: {(90N/6)+ (5Nr/6)}/N = 84,
cancel N, we get, 15+(5/6 b) = 84.
Therefore, B is sufficient, hence, the answer is B.
n= number of people who have given test in person, m= number of people who have given test remotely
we know, (np+mr)/(m+n) = 84, to find: r?
Sol.
Statement 1-> m+n = 30
Here value of m, n can be anything, neither do we know the value or p, thus it is insufficient, cancel option A and D
Statement 2-> n=(m+n)/6, and p = 90, lets take m+n=N
Now, equation becomes: {(90N/6)+ (5Nr/6)}/N = 84,
cancel N, we get, 15+(5/6 b) = 84.
Therefore, B is sufficient, hence, the answer is B.
