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Carlos has 14 coins in his pocket, consisting of quarters and nickels

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Carlos has 14 coins in his pocket, consisting of quarters and nickels [#permalink] New post   24 May 2022, 03:00
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Carlos has 14 coins in his pocket, consisting of quarters and nickels only. The monetary value of these coins is $2.30.

Quantity A
Quantity B
the number of quarters
the number of nickels



A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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A
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rx10
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Re: Carlos has 14 coins in his pocket, consisting of quarters and nickels [#permalink] New post   24 May 2022, 03:22
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Nickel \(= $0.05\)
Quarter \(= $0.25\)

Let's say total nickel \(= x\) so total quarter coin \(= 14 - x\)

Total value \(= $2.30\)

\(0.05x + 0.25(14 - x) = 2.30\)

\(0.05x + 3.5 - 0.25x = 2.30\)

\(1.20 = 0.20x\)

\(x = 6\)

Qt \(A = 8\) & Qt \(B = 6\)

Qt A > Qt B

Answer A
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B
alsafaj
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Carlos has 14 coins in his pocket, consisting of quarters and nickels [#permalink] New post   Updated on: 24 May 2022, 08:31
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Since there are a total of 14 coins (mix of quarters and nickles), then we can experiment:

Assuming all 14 coins are nickles, that gives us a value of $0.70 and the remaining $1.6 are quarters which is got to be at least 7 quarters. Given there is a remainder of 7 coins, nickles can satisfy the remaining value. we can then conclude that # of quarters are > # of nickles.

Answer is (A)

Originally posted by alsafaj on 24 May 2022, 08:28.
Last edited by alsafaj on 24 May 2022, 08:31, edited 1 time in total.
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alsafaj
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Re: Carlos has 14 coins in his pocket, consisting of quarters and nickels [#permalink] New post   24 May 2022, 08:30
rx10 wrote:
Nickel \(= $0.05\)
Quarter \(= $0.25\)

Let's say total nickel \(= x\) so total quarter coin \(= 14 - x\)

Total value \(= $2.30\)

\(0.05x + 0.25(14 - x) = 2.30\)

\(0.05x + 3.5 - 0.25x = 2.30\)

\(1.20 = 0.20x\)

\(x = 6\)

Qt \(A = 8\) & Qt \(B = 6\)

Qt A > Qt B

Answer A


Good approach. I did it a bit differently with logic, but math always make better sense. Thanks!
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gmatclubot
Re: Carlos has 14 coins in his pocket, consisting of quarters and nickels [#permalink]
24 May 2022, 08:30
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