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30 Dec 2023, 22:33
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B
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Difficulty:
95%
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Question Stats:
33% (02:07) correct
67%
(02:10)
wrong
based on 99
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Jingle, an elf, traveled a total of 1,080 miles over the course of three days. Was his daily average (arithmetic mean) distance greater than the median of the distances he covered on these days?
(1) The range of the distances Jingle covered over these days was equal to his daily average (arithmetic mean) distance.
(2) On one of the days, Jingle covered 360 miles.
(1) The range of the distances Jingle covered over these days was equal to his daily average (arithmetic mean) distance.
(2) On one of the days, Jingle covered 360 miles.
30 Dec 2023, 22:33
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Official Solution:
Jingle, an elf, traveled a total of 1,080 miles over the course of three days. Was his daily average (arithmetic mean) distance greater than the median of the distances he covered on these days?
Jingle's total travel of 1,080 miles over three days results in a daily average distance of 1,080/3 = 360 miles. The question then becomes: is the median distance less than 360 miles?
(1) The range of the distances Jingle covered over these days was equal to his daily average (arithmetic mean) distance.
This means the range = 360. Let's consider sets that could yield both a NO and a YES answers.
For distances of 200, 320, and 560 miles, the median of 320 is less than 360.
For distances of 150, 420, and 510 miles, the median of 420 is greater than 360.
Not sufficient.
(2) On one of the days, Jingle covered 360 miles.
Since Jingle covered 360 miles on one of the days, on one of the remaining two days he must have covered a distance less than or equal to 360 miles, and on the other, a distance greater than or equal to 360 miles. This leads to the three distances being {≤360, 360, ≥360}. Therefore, the median, as the middle value, would also be 360, matching the average and yielding a NO answer to the question. Sufficient.
Sufficient.
Answer: B
Jingle, an elf, traveled a total of 1,080 miles over the course of three days. Was his daily average (arithmetic mean) distance greater than the median of the distances he covered on these days?
Jingle's total travel of 1,080 miles over three days results in a daily average distance of 1,080/3 = 360 miles. The question then becomes: is the median distance less than 360 miles?
(1) The range of the distances Jingle covered over these days was equal to his daily average (arithmetic mean) distance.
This means the range = 360. Let's consider sets that could yield both a NO and a YES answers.
For distances of 200, 320, and 560 miles, the median of 320 is less than 360.
For distances of 150, 420, and 510 miles, the median of 420 is greater than 360.
Not sufficient.
(2) On one of the days, Jingle covered 360 miles.
Since Jingle covered 360 miles on one of the days, on one of the remaining two days he must have covered a distance less than or equal to 360 miles, and on the other, a distance greater than or equal to 360 miles. This leads to the three distances being {≤360, 360, ≥360}. Therefore, the median, as the middle value, would also be 360, matching the average and yielding a NO answer to the question. Sufficient.
Sufficient.
Answer: B
18 Apr 2024, 20:38
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Doesn't "The range of the distances Jingle covered over these days was equal to his daily average (arithmetic mean) distance." mean that daily walkin distance was equal to 3-day average? My English is not enough to undestand this sentence.
