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.
Statement 2: divide the expression by 3.
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