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12 Dec 2023, 07:00
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B
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
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.
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.
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13 Dec 2023, 11:56
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GMAT Club Official Explanation:
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.
General Discussion
12 Dec 2023, 07:39
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Given: Jingle, an elf, traveled a total of 1,080 miles over the course of three days.
Asked: Was his daily average (arithmetic mean) distance greater than the median of the distances he covered on these days?
Let the distance travelled on three days be d1, d2 & d3 such that d1 <= d2 <= d3
D = d1 + d2 + d3 = 1080 miles
Is (d1 + d2 + d3)/3 > d2?
Is d2 < 1080/3 = 360 miles ?
(1) The range of the distances Jingle covered over these days was equal to his daily average (arithmetic mean) distance.
d3 - d1 = (d1 + d2 + d3)/3 = 360; d3 = 360+d1
d1, d2, 360+d1; 360 + 2d1 + d2 = 1080; 2d1 + d2 = 720;
Case 1: {d1, d2, d3} = {240, 240, 600}: d2 =240 < 360
Case 2: {d1, d2, d3} = {150, 420, 510}: d2 =420 > 360
NOT SUFFICIENT
(2) On one of the days, Jingle covered 360 miles.
d1=360-x; d2 = 360; d3=360+x; where x is non-negative number.
Median of distance = d2 = 360 = Average of the distance
SUFFICIENT
IMO B
Asked: Was his daily average (arithmetic mean) distance greater than the median of the distances he covered on these days?
Let the distance travelled on three days be d1, d2 & d3 such that d1 <= d2 <= d3
D = d1 + d2 + d3 = 1080 miles
Is (d1 + d2 + d3)/3 > d2?
Is d2 < 1080/3 = 360 miles ?
(1) The range of the distances Jingle covered over these days was equal to his daily average (arithmetic mean) distance.
d3 - d1 = (d1 + d2 + d3)/3 = 360; d3 = 360+d1
d1, d2, 360+d1; 360 + 2d1 + d2 = 1080; 2d1 + d2 = 720;
Case 1: {d1, d2, d3} = {240, 240, 600}: d2 =240 < 360
Case 2: {d1, d2, d3} = {150, 420, 510}: d2 =420 > 360
NOT SUFFICIENT
(2) On one of the days, Jingle covered 360 miles.
d1=360-x; d2 = 360; d3=360+x; where x is non-negative number.
Median of distance = d2 = 360 = Average of the distance
SUFFICIENT
IMO B
