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06 Aug 2026, 11:07
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A stationery shop sells only notebooks and planners. Each notebook sells for $30 and costs the shop $25, while each planner sells for $20 and costs the shop $12. In June, the shop sold 140 notebooks and planners in total. Was the shop’s profit from these sales more than $900?
(1) The shop’s profit from planners was less than its profit from notebooks.
(2) The shop’s revenue from notebooks was greater than its revenue from planners.
(1) The shop’s profit from planners was less than its profit from notebooks.
(2) The shop’s revenue from notebooks was greater than its revenue from planners.
06 Aug 2026, 11:07
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Official Solution:
A stationery shop sells only notebooks and planners. Each notebook sells for $30 and costs the shop $25, while each planner sells for $20 and costs the shop $12. In June, the shop sold 140 notebooks and planners in total. Was the shop’s profit from these sales more than $900?
(1) The shop’s profit from planners was less than its profit from notebooks.
Each notebook gives a profit of $5, and each planner gives a profit of $8.
Let \(p\) be the number of planners sold. Then the number of notebooks sold is \(140 - p\).
Statement (1) gives:
\(8p < 5(140 - p)\)
\(13p < 700\)
\(p < 53.\text{something}\)
So \(p\) can be at most 53.
Since each planner gives more profit than each notebook, the total profit is greatest when \(p\) is as large as possible. Even at the highest possible value, \(p = 53\), the total profit is:
\(53 * 8 + 87 * 5 = 424 + 435 = 859\)
So the profit was not more than $900. The answer to the question is NO.
Sufficient.
(2) The shop’s revenue from notebooks was greater than its revenue from planners.
This gives:
\(30(140 - p) > 20p\)
\(4,200 - 30p > 20p\)
\(4,200 > 50p\)
\(p < 84\)
So \(p\) can be at most 83.
This is not enough. If \(p = 60\), the profit is:
\(60 * 8 + 80 * 5 = 880\)
So the answer is NO.
But if \(p = 80\), the profit is:
\(80 * 8 + 60 * 5 = 940\)
So the answer is YES.
Not sufficient.
Answer: A
A stationery shop sells only notebooks and planners. Each notebook sells for $30 and costs the shop $25, while each planner sells for $20 and costs the shop $12. In June, the shop sold 140 notebooks and planners in total. Was the shop’s profit from these sales more than $900?
(1) The shop’s profit from planners was less than its profit from notebooks.
Each notebook gives a profit of $5, and each planner gives a profit of $8.
Let \(p\) be the number of planners sold. Then the number of notebooks sold is \(140 - p\).
Statement (1) gives:
\(8p < 5(140 - p)\)
\(13p < 700\)
\(p < 53.\text{something}\)
So \(p\) can be at most 53.
Since each planner gives more profit than each notebook, the total profit is greatest when \(p\) is as large as possible. Even at the highest possible value, \(p = 53\), the total profit is:
\(53 * 8 + 87 * 5 = 424 + 435 = 859\)
So the profit was not more than $900. The answer to the question is NO.
Sufficient.
(2) The shop’s revenue from notebooks was greater than its revenue from planners.
This gives:
\(30(140 - p) > 20p\)
\(4,200 - 30p > 20p\)
\(4,200 > 50p\)
\(p < 84\)
So \(p\) can be at most 83.
This is not enough. If \(p = 60\), the profit is:
\(60 * 8 + 80 * 5 = 880\)
So the answer is NO.
But if \(p = 80\), the profit is:
\(80 * 8 + 60 * 5 = 940\)
So the answer is YES.
Not sufficient.
Answer: A
