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06 Aug 2026, 07:46
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A custom print shop produced event posters last year. The shop’s total cost for the posters was $48,000 plus a licensing fee equal to 20% of the shop’s total revenue from poster sales. If the shop sold every poster it produced and its revenue from poster sales was not greater than its total cost for the posters, did the shop sell fewer than 8,000 posters last year?
(1) Last year, the shop sold the posters for an average (arithmetic mean) price greater than $8 per poster.
(2) Last year, the shop’s total revenue from poster sales was less than $55,000.
(1) Last year, the shop sold the posters for an average (arithmetic mean) price greater than $8 per poster.
(2) Last year, the shop’s total revenue from poster sales was less than $55,000.
06 Aug 2026, 07:46
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Official Solution:
A custom print shop produced event posters last year. The shop’s total cost for the posters was $48,000 plus a licensing fee equal to 20% of the shop’s total revenue from poster sales. If the shop sold every poster it produced and its revenue from poster sales was not greater than its total cost for the posters, did the shop sell fewer than 8,000 posters last year?
Let \(R\) be the shop’s total revenue from poster sales. Since revenue was not greater than total cost:
\(R \leq 48,000 + 0.20R\)
\(0.80R \leq 48,000\)
\(R \leq 60,000\)
So the shop’s total revenue from poster sales was at most $60,000.
The question asks whether the shop sold fewer than 8,000 posters.
(1) Last year, the shop sold the posters for an average price greater than $8 per poster.
Since total revenue was at most $60,000 and the average price was greater than $8, the number of posters sold was less than:
\(\frac{60,000}{8} = 7,500\)
So the shop definitely sold fewer than 8,000 posters.
Sufficient.
(2) Last year, the shop’s total revenue from poster sales was less than $55,000.
This gives an upper limit on revenue, but it gives no information about the average price per poster.
For example, if revenue was $54,000 and the average price was $9, then the shop sold 6,000 posters, so the answer is YES.
But if revenue was $54,000 and the average price was $6, then the shop sold 9,000 posters, so the answer is NO.
Not sufficient.
Answer: A
A custom print shop produced event posters last year. The shop’s total cost for the posters was $48,000 plus a licensing fee equal to 20% of the shop’s total revenue from poster sales. If the shop sold every poster it produced and its revenue from poster sales was not greater than its total cost for the posters, did the shop sell fewer than 8,000 posters last year?
Let \(R\) be the shop’s total revenue from poster sales. Since revenue was not greater than total cost:
\(R \leq 48,000 + 0.20R\)
\(0.80R \leq 48,000\)
\(R \leq 60,000\)
So the shop’s total revenue from poster sales was at most $60,000.
The question asks whether the shop sold fewer than 8,000 posters.
(1) Last year, the shop sold the posters for an average price greater than $8 per poster.
Since total revenue was at most $60,000 and the average price was greater than $8, the number of posters sold was less than:
\(\frac{60,000}{8} = 7,500\)
So the shop definitely sold fewer than 8,000 posters.
Sufficient.
(2) Last year, the shop’s total revenue from poster sales was less than $55,000.
This gives an upper limit on revenue, but it gives no information about the average price per poster.
For example, if revenue was $54,000 and the average price was $9, then the shop sold 6,000 posters, so the answer is YES.
But if revenue was $54,000 and the average price was $6, then the shop sold 9,000 posters, so the answer is NO.
Not sufficient.
Answer: A
