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16 Nov 2021, 03:52
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Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?
(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
(2) Porthos height is 190 centimetres
(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
(2) Porthos height is 190 centimetres
16 Nov 2021, 03:52
Kudos
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Official Solution:
Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?
(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
The heights of the three musketeers in ascending order are \(x\), \(x+1\), and \(x+10\). The median is \(x+1\) and the mean is \(\frac{x+(x+1)+(x+10)}{3}=x+3.something\). Obviously the mean (\(x+3.something\)) is greater than the median (\(x+1\)). Sufficient.
(2) Porthos height is 190 centimetres.
Clearly insuficient.
Answer: A
Is the average (arithmetic mean) height of Porthos, Athos, and Aramis greater than the median height of Porthos, Athos, and Aramis?
(1) Porthos is 10 centimetres taller than Athos, and 9 centimeters taller than Aramis.
The heights of the three musketeers in ascending order are \(x\), \(x+1\), and \(x+10\). The median is \(x+1\) and the mean is \(\frac{x+(x+1)+(x+10)}{3}=x+3.something\). Obviously the mean (\(x+3.something\)) is greater than the median (\(x+1\)). Sufficient.
(2) Porthos height is 190 centimetres.
Clearly insuficient.
Answer: A
sunshineeee
04 Dec 2025, 03:26
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I did not quite understand the solution. how about if we put
x, x-9, and x-10 as the heights?
x, x-9, and x-10 as the heights?
