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26 Apr 2026, 13:07
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A tea shop placed 27 sealed jars of loose leaf tea on two shelves. On each shelf, the jars are arranged from lightest to heaviest. If the heaviest jar on the lower shelf weighs 1.18 kg, and the lightest jar on the upper shelf weighs 1.32 kg, what is the median weight of the 27 jars?
(1) The average (arithmetic mean) weight of the 27 jars is 1.25 kg.
(2) The lower shelf holds one more jar than the upper shelf.
(1) The average (arithmetic mean) weight of the 27 jars is 1.25 kg.
(2) The lower shelf holds one more jar than the upper shelf.
26 Apr 2026, 13:07
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Official Solution:
A tea shop placed 27 sealed jars of loose leaf tea on two shelves. On each shelf, the jars are arranged from lightest to heaviest. If the heaviest jar on the lower shelf weighs 1.18 kg, and the lightest jar on the upper shelf weighs 1.32 kg, what is the median weight of the 27 jars?
First, since 27 is odd, the median is the 14th jar when all 27 jar weights are listed from lightest to heaviest.
Next, since on each shelf the jars are arranged from lightest to heaviest, and the heaviest lower shelf jar is 1.18 kg while the lightest upper shelf jar is 1.32 kg, every jar on the lower shelf is lighter than every jar on the upper shelf.
(1) The average arithmetic mean weight of the 27 jars is 1.25 kg.
Knowing the mean is 1.25 kg does not tell us what the 14th jar weighs. Not sufficient.
(2) The lower shelf holds one more jar than the upper shelf.
This implies that the lower shelf holds 14 jars and the upper shelf holds 13 jars. Since every lower shelf jar is lighter than every upper shelf jar, and the heaviest lower shelf jar weighs 1.18 kg, that jar must be the 14th jar overall in the lightest to heaviest ordering. So, the median weight of the 27 jars is 1.18 kg. Sufficient.
Answer: B
A tea shop placed 27 sealed jars of loose leaf tea on two shelves. On each shelf, the jars are arranged from lightest to heaviest. If the heaviest jar on the lower shelf weighs 1.18 kg, and the lightest jar on the upper shelf weighs 1.32 kg, what is the median weight of the 27 jars?
First, since 27 is odd, the median is the 14th jar when all 27 jar weights are listed from lightest to heaviest.
Next, since on each shelf the jars are arranged from lightest to heaviest, and the heaviest lower shelf jar is 1.18 kg while the lightest upper shelf jar is 1.32 kg, every jar on the lower shelf is lighter than every jar on the upper shelf.
(1) The average arithmetic mean weight of the 27 jars is 1.25 kg.
Knowing the mean is 1.25 kg does not tell us what the 14th jar weighs. Not sufficient.
(2) The lower shelf holds one more jar than the upper shelf.
This implies that the lower shelf holds 14 jars and the upper shelf holds 13 jars. Since every lower shelf jar is lighter than every upper shelf jar, and the heaviest lower shelf jar weighs 1.18 kg, that jar must be the 14th jar overall in the lightest to heaviest ordering. So, the median weight of the 27 jars is 1.18 kg. Sufficient.
Answer: B
02 May 2026, 08:24
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I did not quite understand the solution. How do we arrive at the conclusion that since the heaviest jar in the lower shelft is 1.18kg it must be 14th jar overall?
