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06 Aug 2026, 06:23
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At a stationery stall, notebooks, pens, and folders were sold at fixed unit prices. Elena bought 2 notebooks, 5 pens, and 3 folders from the stall for $67. What was the price of one pen?
(1) Sofia bought 4 notebooks and 6 folders from the same stall for $54.
(2) Marcus bought 3 folders from the same stall for $18.
(1) Sofia bought 4 notebooks and 6 folders from the same stall for $54.
(2) Marcus bought 3 folders from the same stall for $18.
06 Aug 2026, 06:23
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Official Solution:
At a stationery stall, notebooks, pens, and folders were sold at fixed unit prices. Elena bought 2 notebooks, 5 pens, and 3 folders from the stall for $67. What was the price of one pen?
Let \(N\), \(P\), and \(F\) be the prices of one notebook, one pen, and one folder, respectively.
From Elena’s purchase:
\(2N + 5P + 3F = 67\)
The question asks for \(P\).
(1) Sofia bought 4 notebooks and 6 folders from the same stall for $54.
So:
\(4N + 6F = 54\)
Divide by 2:
\(2N + 3F = 27\)
From Elena’s equation:
\(2N + 5P + 3F = 67\)
Since \(2N + 3F = 27\):
\(27 + 5P = 67\)
\(5P = 40\)
\(P = 8\)
Sufficient.
(2) Marcus bought 3 folders from the same stall for $18.
So:
\(3F = 18\)
\(F = 6\)
Substitute into Elena’s equation:
\(2N + 5P + 3 * 6 = 67\)
\(2N + 5P = 49\)
This does not determine \(P\).
For example, if \(P = 5\), then:
\(2N + 25 = 49\)
\(N = 12\)
But if \(P = 7\), then:
\(2N + 35 = 49\)
\(N = 7\)
Different values of \(P\) are possible.
Not sufficient.
Answer: A
At a stationery stall, notebooks, pens, and folders were sold at fixed unit prices. Elena bought 2 notebooks, 5 pens, and 3 folders from the stall for $67. What was the price of one pen?
Let \(N\), \(P\), and \(F\) be the prices of one notebook, one pen, and one folder, respectively.
From Elena’s purchase:
\(2N + 5P + 3F = 67\)
The question asks for \(P\).
(1) Sofia bought 4 notebooks and 6 folders from the same stall for $54.
So:
\(4N + 6F = 54\)
Divide by 2:
\(2N + 3F = 27\)
From Elena’s equation:
\(2N + 5P + 3F = 67\)
Since \(2N + 3F = 27\):
\(27 + 5P = 67\)
\(5P = 40\)
\(P = 8\)
Sufficient.
(2) Marcus bought 3 folders from the same stall for $18.
So:
\(3F = 18\)
\(F = 6\)
Substitute into Elena’s equation:
\(2N + 5P + 3 * 6 = 67\)
\(2N + 5P = 49\)
This does not determine \(P\).
For example, if \(P = 5\), then:
\(2N + 25 = 49\)
\(N = 12\)
But if \(P = 7\), then:
\(2N + 35 = 49\)
\(N = 7\)
Different values of \(P\) are possible.
Not sufficient.
Answer: A
