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06 Aug 2026, 07:56
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A logistics coordinator planned a delivery route for a truck. Before the route was driven, she estimated the distance the truck would travel and the amount of fuel it would use, and from those estimates she calculated an estimated fuel efficiency in kilometers per liter. After the route was completed, the actual fuel efficiency was calculated from the actual distance driven and the actual amount of fuel used. Did the estimated fuel efficiency differ from the actual fuel efficiency by at most 20% of the actual fuel efficiency?
(1) The estimated distance differed from the actual distance by at most 20% of the actual distance, and the estimated fuel use differed from the actual fuel use by at most 20% of the actual fuel use.
(2) The coordinator overestimated the distance by 100 kilometers and underestimated the fuel use by 10 liters.
(1) The estimated distance differed from the actual distance by at most 20% of the actual distance, and the estimated fuel use differed from the actual fuel use by at most 20% of the actual fuel use.
(2) The coordinator overestimated the distance by 100 kilometers and underestimated the fuel use by 10 liters.
06 Aug 2026, 07:56
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Official Solution:
A logistics coordinator planned a delivery route for a truck. Before the route was driven, she estimated the distance the truck would travel and the amount of fuel it would use, and from those estimates she calculated an estimated fuel efficiency in kilometers per liter. After the route was completed, the actual fuel efficiency was calculated from the actual distance driven and the actual amount of fuel used. Did the estimated fuel efficiency differ from the actual fuel efficiency by at most 20% of the actual fuel efficiency?
Let \(D\) be the actual distance driven, and let \(F\) be the actual amount of fuel used.
Actual fuel efficiency \(= \frac{D}{F}\)
The question asks whether the estimated fuel efficiency differed from \(\frac{D}{F}\) by at most \(20\%\).
(1) The estimated distance differed from the actual distance by at most \(20\%\), and the estimated fuel use differed from the actual fuel use by at most \(20\%\).
If both estimates were \(20\%\) too high, then the estimated fuel efficiency would be:
\(\frac{1.2D}{1.2F} = \frac{D}{F}\)
The two efficiencies would be equal, so the answer would be YES.
But if the distance estimate was \(20\%\) too high and the fuel-use estimate was \(20\%\) too low, then the estimated fuel efficiency would be:
\(\frac{1.2D}{0.8F} = 1.5 * \frac{D}{F}\)
This is \(50\%\) greater than the actual fuel efficiency, so the answer would be NO.
Not sufficient.
(2) The coordinator overestimated the distance by 100 kilometers and underestimated the fuel use by 10 liters.
This gives the absolute errors, but not the actual distance or actual fuel use.
For example, if \(D = 500\) and \(F = 50\), then:
Actual fuel efficiency \(= \frac{500}{50} = 10\)
Estimated fuel efficiency \(= \frac{500 + 100}{50 - 10} = \frac{600}{40} = 15\)
The estimate is \(50\%\) greater than the actual value, so the answer is NO.
But if \(D = 1,500\) and \(F = 150\), then:
Actual fuel efficiency \(= \frac{1,500}{150} = 10\)
Estimated fuel efficiency \(= \frac{1,500 + 100}{150 - 10} = \frac{1,600}{140} = 11.\text{something}\)
The estimate differs from 10 by less than \(20\%\), so the answer is YES.
Not sufficient.
(1)+(2) The same two examples from statement (2) also satisfy statement (1).
In the first example, 100 is exactly \(20\%\) of 500, and 10 is exactly \(20\%\) of 50.
In the second example, 100 is less than \(20\%\) of 1,500, and 10 is less than \(20\%\) of 150.
So both statements together can still give either NO or YES.
Not sufficient.
Answer: E
A logistics coordinator planned a delivery route for a truck. Before the route was driven, she estimated the distance the truck would travel and the amount of fuel it would use, and from those estimates she calculated an estimated fuel efficiency in kilometers per liter. After the route was completed, the actual fuel efficiency was calculated from the actual distance driven and the actual amount of fuel used. Did the estimated fuel efficiency differ from the actual fuel efficiency by at most 20% of the actual fuel efficiency?
Let \(D\) be the actual distance driven, and let \(F\) be the actual amount of fuel used.
Actual fuel efficiency \(= \frac{D}{F}\)
The question asks whether the estimated fuel efficiency differed from \(\frac{D}{F}\) by at most \(20\%\).
(1) The estimated distance differed from the actual distance by at most \(20\%\), and the estimated fuel use differed from the actual fuel use by at most \(20\%\).
If both estimates were \(20\%\) too high, then the estimated fuel efficiency would be:
\(\frac{1.2D}{1.2F} = \frac{D}{F}\)
The two efficiencies would be equal, so the answer would be YES.
But if the distance estimate was \(20\%\) too high and the fuel-use estimate was \(20\%\) too low, then the estimated fuel efficiency would be:
\(\frac{1.2D}{0.8F} = 1.5 * \frac{D}{F}\)
This is \(50\%\) greater than the actual fuel efficiency, so the answer would be NO.
Not sufficient.
(2) The coordinator overestimated the distance by 100 kilometers and underestimated the fuel use by 10 liters.
This gives the absolute errors, but not the actual distance or actual fuel use.
For example, if \(D = 500\) and \(F = 50\), then:
Actual fuel efficiency \(= \frac{500}{50} = 10\)
Estimated fuel efficiency \(= \frac{500 + 100}{50 - 10} = \frac{600}{40} = 15\)
The estimate is \(50\%\) greater than the actual value, so the answer is NO.
But if \(D = 1,500\) and \(F = 150\), then:
Actual fuel efficiency \(= \frac{1,500}{150} = 10\)
Estimated fuel efficiency \(= \frac{1,500 + 100}{150 - 10} = \frac{1,600}{140} = 11.\text{something}\)
The estimate differs from 10 by less than \(20\%\), so the answer is YES.
Not sufficient.
(1)+(2) The same two examples from statement (2) also satisfy statement (1).
In the first example, 100 is exactly \(20\%\) of 500, and 10 is exactly \(20\%\) of 50.
In the second example, 100 is less than \(20\%\) of 1,500, and 10 is less than \(20\%\) of 150.
So both statements together can still give either NO or YES.
Not sufficient.
Answer: E
