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03 Aug 2026, 08:11
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Before the start of the fall service cycle, the city transit authority revised Route G by increasing service frequency and adding a stop near a busy office district. Based on those changes, the authority expected the average (arithmetic mean) number of riders on Route G each weekday to increase by 20 percent. Did the average (arithmetic mean) number of riders on Route G each weekday actually increase by more than 25 percent?
(1) The actual average (arithmetic mean) number of riders on Route G each weekday was 500 higher than expected.
(2) The actual average (arithmetic mean) number of riders on Route G each weekday was less than 12,600.
(1) The actual average (arithmetic mean) number of riders on Route G each weekday was 500 higher than expected.
(2) The actual average (arithmetic mean) number of riders on Route G each weekday was less than 12,600.
03 Aug 2026, 08:11
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Official Solution:
Before the start of the fall service cycle, the city transit authority revised Route G by increasing service frequency and adding a stop near a busy office district. Based on those changes, the authority expected the average (arithmetic mean) number of riders on Route G each weekday to increase by 20 percent. Did the average (arithmetic mean) number of riders on Route G each weekday actually increase by more than 25 percent?
Let \(r\) be the original average number of riders on Route G each weekday. Then the expected new average was \(1.2r\).
We need to know whether the actual new average was greater than \(1.25r\).
(1) The actual average (arithmetic mean) number of riders on Route G each weekday was 500 higher than expected.
So the actual average was \(1.2r + 500\)
We need to know whether \(1.2r + 500 > 1.25r\):
\(500 > 0.05r\)
\(r < 10,000\)
Since \(r\) is not determined, the answer cannot be determined. Not sufficient.
(2) The actual average (arithmetic mean) number of riders on Route G each weekday was less than 12,600.
This gives only an upper bound on the actual average. By itself, it does not tell us whether the increase was more than 25 percent. Not sufficient.
(1) + (2) From statement (1), the actual average was \(1.2r + 500\). Using statement (2):
\(1.2r + 500 < 12,600\)
\(1.2r < 12,100\)
\(r < \frac{12,100}{1.2}\)
Since \(\frac{12,100}{1.2} > 10,000\), from \(r < \frac{12,100}{1.2}\), \(r\) may be greater than \(10,000\) or less than \(10,000\). Not sufficient.
Answer: E
Before the start of the fall service cycle, the city transit authority revised Route G by increasing service frequency and adding a stop near a busy office district. Based on those changes, the authority expected the average (arithmetic mean) number of riders on Route G each weekday to increase by 20 percent. Did the average (arithmetic mean) number of riders on Route G each weekday actually increase by more than 25 percent?
Let \(r\) be the original average number of riders on Route G each weekday. Then the expected new average was \(1.2r\).
We need to know whether the actual new average was greater than \(1.25r\).
(1) The actual average (arithmetic mean) number of riders on Route G each weekday was 500 higher than expected.
So the actual average was \(1.2r + 500\)
We need to know whether \(1.2r + 500 > 1.25r\):
\(500 > 0.05r\)
\(r < 10,000\)
Since \(r\) is not determined, the answer cannot be determined. Not sufficient.
(2) The actual average (arithmetic mean) number of riders on Route G each weekday was less than 12,600.
This gives only an upper bound on the actual average. By itself, it does not tell us whether the increase was more than 25 percent. Not sufficient.
(1) + (2) From statement (1), the actual average was \(1.2r + 500\). Using statement (2):
\(1.2r + 500 < 12,600\)
\(1.2r < 12,100\)
\(r < \frac{12,100}{1.2}\)
Since \(\frac{12,100}{1.2} > 10,000\), from \(r < \frac{12,100}{1.2}\), \(r\) may be greater than \(10,000\) or less than \(10,000\). Not sufficient.
Answer: E
