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06 Aug 2026, 06:04
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A warehouse uses Metro Courier to ship parcels. Metro Courier charges $12 per parcel for the first 12 parcels shipped in a day and $8 for each parcel after the first 12. If the warehouse used only Metro Courier on Tuesday, did the warehouse ship more than 40 parcels on Tuesday?
(1) If the warehouse had shipped 3 additional parcels on Tuesday, its shipping cost for that day would have been at least $400.
(2) The warehouse’s average (arithmetic mean) shipping cost per parcel on Tuesday was $9.
(1) If the warehouse had shipped 3 additional parcels on Tuesday, its shipping cost for that day would have been at least $400.
(2) The warehouse’s average (arithmetic mean) shipping cost per parcel on Tuesday was $9.
06 Aug 2026, 06:04
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Official Solution:
A warehouse uses Metro Courier to ship parcels. Metro Courier charges $12 per parcel for the first 12 parcels shipped in a day and $8 for each parcel after the first 12. If the warehouse used only Metro Courier on Tuesday, did the warehouse ship more than 40 parcels on Tuesday?
Let \(n\) be the number of parcels shipped on Tuesday. The question asks whether \(n > 40\). For more than 12 parcels, the shipping cost is:
\(12 * 12 + 8(n - 12) = 8n + 48\)
(1) If the warehouse had shipped 3 additional parcels on Tuesday, its shipping cost for that day would have been at least $400.
Since $400 is more than \(12 * 12 = 144\), the hypothetical shipment of \(n + 3\) parcels must have included more than 12 parcels. So, the cost would have been:
\(8(n + 3) + 48 = 8n + 72\)
Statement (1) says:
\(8n + 72 \geq 400\)
\(8n \geq 328\)
\(n \geq 41\)
So \(n > 40\).
Sufficient.
(2) The warehouse’s average shipping cost per parcel on Tuesday was $9.
Since the average cost per parcel was $9, the warehouse must have shipped more than 12 parcels; otherwise, the average cost per parcel would have been $12.
So:
\(\frac{8n + 48}{n} = 9\)
\(8n + 48 = 9n\)
\(n = 48\)
So \(n > 40\).
Sufficient.
Answer: D
A warehouse uses Metro Courier to ship parcels. Metro Courier charges $12 per parcel for the first 12 parcels shipped in a day and $8 for each parcel after the first 12. If the warehouse used only Metro Courier on Tuesday, did the warehouse ship more than 40 parcels on Tuesday?
Let \(n\) be the number of parcels shipped on Tuesday. The question asks whether \(n > 40\). For more than 12 parcels, the shipping cost is:
\(12 * 12 + 8(n - 12) = 8n + 48\)
(1) If the warehouse had shipped 3 additional parcels on Tuesday, its shipping cost for that day would have been at least $400.
Since $400 is more than \(12 * 12 = 144\), the hypothetical shipment of \(n + 3\) parcels must have included more than 12 parcels. So, the cost would have been:
\(8(n + 3) + 48 = 8n + 72\)
Statement (1) says:
\(8n + 72 \geq 400\)
\(8n \geq 328\)
\(n \geq 41\)
So \(n > 40\).
Sufficient.
(2) The warehouse’s average shipping cost per parcel on Tuesday was $9.
Since the average cost per parcel was $9, the warehouse must have shipped more than 12 parcels; otherwise, the average cost per parcel would have been $12.
So:
\(\frac{8n + 48}{n} = 9\)
\(8n + 48 = 9n\)
\(n = 48\)
So \(n > 40\).
Sufficient.
Answer: D
