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Last year Charles spent $24,000 total on rare coins, stamps, and books

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Last year Charles spent $24,000 total on rare coins, stamps, and books  [#permalink]

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New post 17 Oct 2019, 01:52
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  35% (medium)

Question Stats:

73% (01:31) correct 27% (01:29) wrong based on 14 sessions

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Last year Charles spent $24,000 total on rare coins, stamps, and books. How much did he spend on rare stamps?

(1) Last year, the amount that Charles spent on stamps and coins combined was five times the amount he spent on books.
(2) Last year, the amount Charles spent on coins was three times the amount spent on stamps and books combined.

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Re: Last year Charles spent $24,000 total on rare coins, stamps, and books  [#permalink]

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New post 17 Oct 2019, 05:36
from the given, \(c+s+b = 24000\), s = ?

from statement (1), \(c+s = 5b\),
then \(6b = 24000\), and \(b = 4000\)
so \(c+s = 20000\) ---> we can't know s alone (insufficient)

from statement (2), \(c = 3(s+b)\),
then \(\frac{4}{3}c = 24000\), and \(c = 18000\)
so \(s+b = 6000\) -----> we can't know s alone (insufficient)

But from combining (1) and (2), \(s = 2000\)
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Re: Last year Charles spent $24,000 total on rare coins, stamps, and books   [#permalink] 17 Oct 2019, 05:36
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Last year Charles spent $24,000 total on rare coins, stamps, and books

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