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A courier company assigned each of its drivers to exactly one of three delivery zones: Harbor, Central, or Ridge. If the numbers of drivers in Harbor, Central, and Ridge were in the ratio \(2:3:5\), respectively, was the average number of packages delivered per driver across all three zones combined greater than 30?
(1) The average numbers of packages delivered per driver in Harbor, Central, and Ridge were 38, 27, and 25, respectively.
(2) The total number of packages delivered by all the drivers was less than 300.
(1) The average numbers of packages delivered per driver in Harbor, Central, and Ridge were 38, 27, and 25, respectively.
(2) The total number of packages delivered by all the drivers was less than 300.
03 Aug 2026, 09:08
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Official Solution:
A courier company assigned each of its drivers to exactly one of three delivery zones: Harbor, Central, or Ridge. If the numbers of drivers in Harbor, Central, and Ridge were in the ratio \(2:3:5\), respectively, was the average number of packages delivered per driver across all three zones combined greater than 30?
(1) The average numbers of packages delivered per driver in Harbor, Central, and Ridge were 38, 27, and 25, respectively.
Let the numbers of drivers in Harbor, Central, and Ridge be \(2k\), \(3k\), and \(5k\). Then the overall average number of packages delivered per driver is:
\(\frac{2k * 38 + 3k * 27 + 5k * 25}{2k + 3k + 5k} =\)
\(= \frac{76k + 81k + 125k}{10k} =\)
\(= 28.2\)
Since \(28.2\) is not greater than \(30\), the answer to the question is no.
Sufficient.
(2) The total number of packages delivered by all the drivers was less than 300.
Again let the numbers of drivers be \(2k\), \(3k\), and \(5k\). Then the total number of drivers is \(10k\).
The total number of packages delivered is less than 300, so the overall average number of packages delivered per driver is less than \(\frac{300}{10k}\).
Since \(k\) is a positive integer, \(10k\) is at least 10. Therefore, the overall average must be less than \(\frac{300}{10} = 30\).
So the answer to the question is definitely no.
Sufficient.
Answer: D
A courier company assigned each of its drivers to exactly one of three delivery zones: Harbor, Central, or Ridge. If the numbers of drivers in Harbor, Central, and Ridge were in the ratio \(2:3:5\), respectively, was the average number of packages delivered per driver across all three zones combined greater than 30?
(1) The average numbers of packages delivered per driver in Harbor, Central, and Ridge were 38, 27, and 25, respectively.
Let the numbers of drivers in Harbor, Central, and Ridge be \(2k\), \(3k\), and \(5k\). Then the overall average number of packages delivered per driver is:
\(\frac{2k * 38 + 3k * 27 + 5k * 25}{2k + 3k + 5k} =\)
\(= \frac{76k + 81k + 125k}{10k} =\)
\(= 28.2\)
Since \(28.2\) is not greater than \(30\), the answer to the question is no.
Sufficient.
(2) The total number of packages delivered by all the drivers was less than 300.
Again let the numbers of drivers be \(2k\), \(3k\), and \(5k\). Then the total number of drivers is \(10k\).
The total number of packages delivered is less than 300, so the overall average number of packages delivered per driver is less than \(\frac{300}{10k}\).
Since \(k\) is a positive integer, \(10k\) is at least 10. Therefore, the overall average must be less than \(\frac{300}{10} = 30\).
So the answer to the question is definitely no.
Sufficient.
Answer: D
