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13 Jan 2026, 10:14
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At a certain shipping depot, each package has a weight recorded in grams. How many packages in the depot weigh more than 420 grams?
(1) The average (arithmetic mean) weight per package is equal to the weight of the lightest package.
(2) The median weight of all the packages in the depot is 410 grams.
(1) The average (arithmetic mean) weight per package is equal to the weight of the lightest package.
(2) The median weight of all the packages in the depot is 410 grams.
13 Jan 2026, 10:14
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Official Solution:
At a certain shipping depot, each package has a weight recorded in grams. How many packages in the depot weigh more than 420 grams?
(1) The average (arithmetic mean) weight per package is equal to the weight of the lightest package.
If the average weight equals the lightest weight, then all packages must have the same weight. But we do not know what that weight is, and we do not know how many packages there are. Not sufficient.
(2) The median weight of all the packages in the depot is 410 grams.
A median of 410 grams does not tell us how many packages are above 420 grams. Depending on the distribution and the number of packages, the count above 420 could vary. Not sufficient.
(1)+(2) From (1), all packages have the same weight. If the median is 410 grams, that common weight must be 410 grams. So all packages, however many there are, weigh 410 grams. Therefore, no packages weigh more than 420 grams. Sufficient.
Answer: C
At a certain shipping depot, each package has a weight recorded in grams. How many packages in the depot weigh more than 420 grams?
(1) The average (arithmetic mean) weight per package is equal to the weight of the lightest package.
If the average weight equals the lightest weight, then all packages must have the same weight. But we do not know what that weight is, and we do not know how many packages there are. Not sufficient.
(2) The median weight of all the packages in the depot is 410 grams.
A median of 410 grams does not tell us how many packages are above 420 grams. Depending on the distribution and the number of packages, the count above 420 could vary. Not sufficient.
(1)+(2) From (1), all packages have the same weight. If the median is 410 grams, that common weight must be 410 grams. So all packages, however many there are, weigh 410 grams. Therefore, no packages weigh more than 420 grams. Sufficient.
Answer: C
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Schools: Stanford HBS CBS Haas '26 Kellogg '26 Darden '26 Wharton '26
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24 Feb 2026, 07:53
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I like the solution - it’s helpful.
