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A casino pays players using purple and orange chips; each

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A casino pays players using purple and orange chips; each [#permalink]

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A casino pays players using purple and orange chips; each purple chip is worth p dollars, and each orange chip is worth n dollars. If p and n are integers, what is the combined value of two purple chip and one orange chip?

(1) The combined value of five purple chips and seven orange chips is 53 dollars.
(2) The combined value of six purple chips and three orange chips is 42 dollars.

Source: Manhattan GMAT - Thursdays with Ron (September 13, 2012)
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Jan 2013, 05:06, edited 1 time in total.
Renamed the topic, edited the question and the tags.

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Re: Casino Chips [#permalink]

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le7els wrote:
Source: Manhattan GMAT - Thursdays with Ron (September 13, 2012)

A casino pays players using purple and orange chips; each purple chip is worth p dollars, and each orange chip is worth n dollars. If p and n are integers, what is the combined value of two purple chip and one orange chip?

(1) The combined value of five purple chips and seven orange chips is 53 dollars.
(2) The combined value of six purple chips and three orange chips is 42 dollars.


The question is:what is the value of 2p+n?

Statement 1: 5p+7n=53
since it is given that p and n are integers, therefore \(p=(53-7n)/5\). For p to be an integer, 53-7n has to be an integer or 7n has to be such a number which ends up with 8 at its units place. Only \(7x4=28\) does that. Hence n=4, and p comes out as 5.
Sufficient.

Statement 2: divide the expression by 3.
Sufficient.

+1D
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Re: A casino pays players using purple and orange chips; each [#permalink]

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A casino pays players using purple and orange chips; each purple chip is worth p dollars, and each orange chip is worth n dollars. If p and n are integers, what is the combined value of two purple chip and one orange chip?

Questions: 2p+n=?

(1) The combined value of five purple chips and seven orange chips is 53 dollars --> \(5p+7n=53\) --> \(5p=53-7n\). Thus we have that 53 minus multiple of 7 must be a multiple of 5. Only positive integer values of p and n which satisfy this are 5 and 4, respectively. Sufficient.

(2) The combined value of six purple chips and three orange chips is 42 dollars --> \(6p+3n=42\) --> reduce by 3: \(2p+n=14\). Sufficient.

Answer: D.

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Hope it helps.
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Re: A casino pays players using purple and orange chips; each [#permalink]

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New post 08 Feb 2013, 00:51
Thanks a lot for your help, Marcab & Bunuel. My apologies regarding the classification issue.

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Re: A casino pays players using purple and orange chips; each [#permalink]

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Re: A casino pays players using purple and orange chips; each   [#permalink] 12 Nov 2014, 05:05
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