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06 Aug 2026, 08:10
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At a theater concession stand, only snack boxes and meal boxes were sold during an afternoon event. Each snack box sold for $12, and each meal box sold for $20. Did the stand sell more snack boxes than meal boxes that afternoon?
(1) The average (arithmetic mean) selling price per box sold that afternoon was $17.
(2) The median selling price per box sold that afternoon was $20.
(1) The average (arithmetic mean) selling price per box sold that afternoon was $17.
(2) The median selling price per box sold that afternoon was $20.
06 Aug 2026, 08:10
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Official Solution:
At a theater concession stand, only snack boxes and meal boxes were sold during an afternoon event. Each snack box sold for $12, and each meal box sold for $20. Did the stand sell more snack boxes than meal boxes that afternoon?
Let \(S\) be the number of snack boxes sold, and let \(M\) be the number of meal boxes sold.
The question asks whether \(S > M\).
(1) The average selling price per box sold that afternoon was $17.
The two possible prices were $12 and $20. Since $17 is closer to $20 than to $12, more meal boxes than snack boxes must have been sold to pull the average closer to $20.
So \(M > S\), and the answer to the question is NO.
Sufficient.
(2) The median selling price per box sold that afternoon was $20.
When the prices are arranged in order, all the $12 values come before all the $20 values.
If snack boxes outnumbered meal boxes, the median would be $12. If the two types were sold in equal numbers, the median would be:
\(\frac{12 + 20}{2} = 16\)
Therefore, for the median to be $20, meal boxes must have outnumbered snack boxes.
So \(M > S\), and the answer to the question is NO.
Sufficient.
Answer: D
At a theater concession stand, only snack boxes and meal boxes were sold during an afternoon event. Each snack box sold for $12, and each meal box sold for $20. Did the stand sell more snack boxes than meal boxes that afternoon?
Let \(S\) be the number of snack boxes sold, and let \(M\) be the number of meal boxes sold.
The question asks whether \(S > M\).
(1) The average selling price per box sold that afternoon was $17.
The two possible prices were $12 and $20. Since $17 is closer to $20 than to $12, more meal boxes than snack boxes must have been sold to pull the average closer to $20.
So \(M > S\), and the answer to the question is NO.
Sufficient.
(2) The median selling price per box sold that afternoon was $20.
When the prices are arranged in order, all the $12 values come before all the $20 values.
If snack boxes outnumbered meal boxes, the median would be $12. If the two types were sold in equal numbers, the median would be:
\(\frac{12 + 20}{2} = 16\)
Therefore, for the median to be $20, meal boxes must have outnumbered snack boxes.
So \(M > S\), and the answer to the question is NO.
Sufficient.
Answer: D
