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05 Aug 2026, 23:15
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At a stationery shop, Nora spent $84 on sketchbooks and colored markers. Each sketchbook cost $12, and each colored marker cost $8. If Nora bought at least one sketchbook and at least one colored marker, how many sketchbooks did she buy?
(1) Nora spent more than $24 on sketchbooks.
(2) Nora spent more than $48 on colored markers.
(1) Nora spent more than $24 on sketchbooks.
(2) Nora spent more than $48 on colored markers.
05 Aug 2026, 23:15
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Official Solution:
At a stationery shop, Nora spent $84 on sketchbooks and colored markers. Each sketchbook cost $12, and each colored marker cost $8. If Nora bought at least one sketchbook and at least one colored marker, how many sketchbooks did she buy?
Let \(S\) be the number of sketchbooks and \(M\) be the number of colored markers. The total cost was $84, so:
\(12S + 8M = 84\)
\(3S + 2M = 21\)
The question asks for \(S\).
(1) Nora spent more than $24 on sketchbooks.
Since each sketchbook cost $12:
\(12S > 24\)
\(S > 2\)
This is not enough.
If \(S = 3\), then:
\(3 * 3 + 2M = 21\)
\(M = 6\)
But if \(S = 5\), then:
\(3 * 5 + 2M = 21\)
\(M = 3\)
Different values of \(S\) are possible.
Not sufficient.
(2) Nora spent more than $48 on colored markers.
Since each colored marker cost $8:
\(8M > 48\)
\(M > 6\)
From \(3S + 2M = 21\), since \(3S\) and 21 are multiples of 3, \(2M\) must also be a multiple of 3. Therefore, \(M\) must be a multiple of 3. Since \(M > 6\), the first possible value is \(M = 9\). The next possible multiple of 3 is \(M = 12\), but then \(2M = 24\), which is already greater than 21. So \(M\) must be 9. Then:
\(3S + 2 * 9 = 21\)
\(S = 1\)
Sufficient.
Answer: B
At a stationery shop, Nora spent $84 on sketchbooks and colored markers. Each sketchbook cost $12, and each colored marker cost $8. If Nora bought at least one sketchbook and at least one colored marker, how many sketchbooks did she buy?
Let \(S\) be the number of sketchbooks and \(M\) be the number of colored markers. The total cost was $84, so:
\(12S + 8M = 84\)
\(3S + 2M = 21\)
The question asks for \(S\).
(1) Nora spent more than $24 on sketchbooks.
Since each sketchbook cost $12:
\(12S > 24\)
\(S > 2\)
This is not enough.
If \(S = 3\), then:
\(3 * 3 + 2M = 21\)
\(M = 6\)
But if \(S = 5\), then:
\(3 * 5 + 2M = 21\)
\(M = 3\)
Different values of \(S\) are possible.
Not sufficient.
(2) Nora spent more than $48 on colored markers.
Since each colored marker cost $8:
\(8M > 48\)
\(M > 6\)
From \(3S + 2M = 21\), since \(3S\) and 21 are multiples of 3, \(2M\) must also be a multiple of 3. Therefore, \(M\) must be a multiple of 3. Since \(M > 6\), the first possible value is \(M = 9\). The next possible multiple of 3 is \(M = 12\), but then \(2M = 24\), which is already greater than 21. So \(M\) must be 9. Then:
\(3S + 2 * 9 = 21\)
\(S = 1\)
Sufficient.
Answer: B
