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06 Aug 2026, 11:04
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During a 10-day craft fair, a print studio sold only posters and banners. Each poster sold for $18 and cost $10 to produce, while each banner sold for $30 and cost $16 to produce. If the studio sold 110 posters and banners in total during the fair, was its profit from these sales more than $1,200?
(1) The studio used 290 ounces of ink to produce the items sold, with each poster requiring 1 ounce and each banner requiring 4 ounces.
(2) The studio sold more banners than posters.
(1) The studio used 290 ounces of ink to produce the items sold, with each poster requiring 1 ounce and each banner requiring 4 ounces.
(2) The studio sold more banners than posters.
06 Aug 2026, 11:04
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Official Solution:
During a 10-day craft fair, a print studio sold only posters and banners. Each poster sold for $18 and cost $10 to produce, while each banner sold for $30 and cost $16 to produce. If the studio sold 110 posters and banners in total during the fair, was its profit from these sales more than $1,200?
(1) The studio used 290 ounces of ink to produce the items sold, with each poster requiring 1 ounce and each banner requiring 4 ounces.
Let \(b\) be the number of banners sold. Since 110 items were sold in total, the number of posters sold was \(110 - b\).
So:
\(1 * (110 - b) + 4b = 290\)
\(110 + 3b = 290\)
\(b = 60\)
Thus, the studio sold 60 banners and 50 posters.
Each poster gave a profit of:
\(18 - 10 = 8\) dollars
Each banner gave a profit of:
\(30 - 16 = 14\) dollars
So the total profit was:
\(50 * 8 + 60 * 14 = 400 + 840 = 1,240\)
Since $1,240 is more than $1,200, the answer is YES.
Sufficient.
(2) The studio sold more banners than posters.
Since 110 items were sold in total, the smallest possible number of banners was 56.
Since each banner gave more profit than each poster, the total profit was lowest when the number of banners was as small as possible.
At 56 banners and 54 posters, the profit was:
\(56 * 14 + 54 * 8 = 784 + 432 = 1,216\)
Since even the lowest possible profit was more than $1,200, the answer is YES.
Sufficient.
Answer: D
During a 10-day craft fair, a print studio sold only posters and banners. Each poster sold for $18 and cost $10 to produce, while each banner sold for $30 and cost $16 to produce. If the studio sold 110 posters and banners in total during the fair, was its profit from these sales more than $1,200?
(1) The studio used 290 ounces of ink to produce the items sold, with each poster requiring 1 ounce and each banner requiring 4 ounces.
Let \(b\) be the number of banners sold. Since 110 items were sold in total, the number of posters sold was \(110 - b\).
So:
\(1 * (110 - b) + 4b = 290\)
\(110 + 3b = 290\)
\(b = 60\)
Thus, the studio sold 60 banners and 50 posters.
Each poster gave a profit of:
\(18 - 10 = 8\) dollars
Each banner gave a profit of:
\(30 - 16 = 14\) dollars
So the total profit was:
\(50 * 8 + 60 * 14 = 400 + 840 = 1,240\)
Since $1,240 is more than $1,200, the answer is YES.
Sufficient.
(2) The studio sold more banners than posters.
Since 110 items were sold in total, the smallest possible number of banners was 56.
Since each banner gave more profit than each poster, the total profit was lowest when the number of banners was as small as possible.
At 56 banners and 54 posters, the profit was:
\(56 * 14 + 54 * 8 = 784 + 432 = 1,216\)
Since even the lowest possible profit was more than $1,200, the answer is YES.
Sufficient.
Answer: D
