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A team of seven robots can complete a data-labeling task in 30
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16 Aug 2026, 13:16
16 Aug 2026, 13:16
Expert Reply
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Question Stats:
50% (04:21) correct
50% (02:48) wrong based on 2 sessions
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A team of seven robots can complete a data-labeling task in 30 hours when working simultaneously. Three of the robots each require k hours to complete the task alone, two other robots each require 2 k hours alone, and the remaining two robots each require 3 k hours alone. What is the difference between the mean and the median of the seven robots' individual completion times?
(A) 20
(B) 40
(C) 56
(D) 60
(E) 80
(A) 20
(B) 40
(C) 56
(D) 60
(E) 80
- Part of the project: GRE Daily Quant Challenge ALL 4 CORE QUANT AREAS
- Also replying to the unanswered questions
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A team of seven robots can complete a data-labeling task in 30
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26 Aug 2026, 00:38
26 Aug 2026, 00:38
Expert Reply
Solution
You don’t actually need to find all seven times.
The individual times are in the ratio: 1:1:1:2:2:3:3
So let the times be those ratios multiplied by \(k\)
Find \(k\) from the combined rate
Since they finish in 30 hours:
\(\frac{3}{k}+\frac{2}{2k}+\frac{2}{3k}=\frac1{30}\)
Simplify:
\(\frac{14}{3k}=\frac1{30}\)
\(k=140\)
Now, use the ratio to get mean and median
The median is the 4th value:
\(2k=280\)
The mean is:
\(\frac{3k+4k+6k}{7}=\frac{13k}{7}\)
So the difference is:
\(2k-\frac{13k}{7} =\frac{k}{7}\)
Since \(k=140:\)
\(\frac{140}{7}=20\)
Fastest approach: recognize the ratio 1:1:1:2:2:3:3, find k, then calculate median − mean = \(\frac{k}{7}\).
Answer: A
You don’t actually need to find all seven times.
The individual times are in the ratio: 1:1:1:2:2:3:3
So let the times be those ratios multiplied by \(k\)
Find \(k\) from the combined rate
Since they finish in 30 hours:
\(\frac{3}{k}+\frac{2}{2k}+\frac{2}{3k}=\frac1{30}\)
Simplify:
\(\frac{14}{3k}=\frac1{30}\)
\(k=140\)
Now, use the ratio to get mean and median
The median is the 4th value:
\(2k=280\)
The mean is:
\(\frac{3k+4k+6k}{7}=\frac{13k}{7}\)
So the difference is:
\(2k-\frac{13k}{7} =\frac{k}{7}\)
Since \(k=140:\)
\(\frac{140}{7}=20\)
Fastest approach: recognize the ratio 1:1:1:2:2:3:3, find k, then calculate median − mean = \(\frac{k}{7}\).
Answer: A
gmatclubot
A team of seven robots can complete a data-labeling task in 30 [#permalink]
26 Aug 2026, 00:38
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