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02 Mar 2026, 04:50
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B
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Difficulty:
45%
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Question Stats:
72% (01:54) correct
28%
(02:38)
wrong
based on 87
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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.
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10 Mar 2026, 03:45
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GMAT Club 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.
General Discussion
02 Mar 2026, 14:59
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1. Identify the Target (The Median) - Total Jars: 27. Median Position: (27+1)/2 = 14th one. Goal: Find the weight of the 14th jar when all 27 are lined up from lightest to heaviest.
2. Analyze the Range - Lower Shelf: The heaviest jar is 1.18 kg. Upper Shelf: The lightest jar is 1.32 kg. Conclusion: Since 1.18 < 1.32, all jars on the lower shelf are lighter than all jars on the upper shelf. The lower shelf represents the first group in our sorted list.
Statement (1): Average is 1.25 kg
Insufficient. Knowing the average (mean) does not tell us the weight of the specific 14th jar. The distribution of weights could change significantly while the average remains 1.25.
Statement (2): Lower shelf has one more jar than upper shelf. Set up the math: Let L be the number of jars on the lower shelf and U be the number on the upper shelf. L + U = 27, L = U + 1. Let's solve: (U + 1) + U = 27, 2U = 26, U = 13 and L = 14. (Or simply - 27/2 = 13.5, so if the first shelf has one more jar than the second, then the first one is 14 and the seccond is 13 (14+13) = 27. Connect to Median: If there are 14 jars on the lower shelf, the 14th jar (the median) is the heaviest jar on the lower shelf. Result: We are told the heaviest jar on the lower shelf is 1.18 kg. Sufficient.
2. Analyze the Range - Lower Shelf: The heaviest jar is 1.18 kg. Upper Shelf: The lightest jar is 1.32 kg. Conclusion: Since 1.18 < 1.32, all jars on the lower shelf are lighter than all jars on the upper shelf. The lower shelf represents the first group in our sorted list.
Statement (1): Average is 1.25 kg
Insufficient. Knowing the average (mean) does not tell us the weight of the specific 14th jar. The distribution of weights could change significantly while the average remains 1.25.
Statement (2): Lower shelf has one more jar than upper shelf. Set up the math: Let L be the number of jars on the lower shelf and U be the number on the upper shelf. L + U = 27, L = U + 1. Let's solve: (U + 1) + U = 27, 2U = 26, U = 13 and L = 14. (Or simply - 27/2 = 13.5, so if the first shelf has one more jar than the second, then the first one is 14 and the seccond is 13 (14+13) = 27. Connect to Median: If there are 14 jars on the lower shelf, the 14th jar (the median) is the heaviest jar on the lower shelf. Result: We are told the heaviest jar on the lower shelf is 1.18 kg. Sufficient.
