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21 Apr 2012, 09:45
catty2004 wrote:
Bunuel wrote:

Joanna bought only $0.15 stamps and$0.29 stamps. How many $0.15 stamps did she buy? Let $$x$$ be the # of$0.15 stamps and $$y$$ the # of $0.29 stamps. Note that $$x$$ and $$y$$ must be an integers. Q: $$x=?$$ (1) She bought$4.40 worth of stamps --> $$15x+29y=440$$. Only one integer combination of $$x$$ and $$y$$ is possible to satisfy $$15x+29y=440$$: $$x=10$$ and $$y=10$$. Sufficient.

(2) She bought an equal number of $0.15 stamps and$0.29 stamps --> $$x=y$$. Not sufficient.

So when we have equation of a type $$ax+by=c$$ and we know that x and y are integers, there can be multiple solutions possible for x and y (eg $$5x+6y=12900$$) OR just one combination (eg $$15x+29y=440$$). Hence in some cases $$ax+by=c$$ is NOT sufficient and in some cases it's sufficient.

Hope it helps.

How can one identify one or multiple solution for $$ax+by=c$$? (i.e. how did you arrive at the conclusion that only one integer combo satisfy $$15x+29y=440$$?

Trial and error plus some logic and knowledge of basics of number properties should help you to identify this.

For more on this type of questions check:
eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html
martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html
a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html
joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html
a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html
joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html

Hope it helps.
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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] ### Show Tags 12 Oct 2012, 20:20 Mixing trial and error with number properties would save you some time. (In relation to the question with 0.15 and 0.29 stamps). The option says 0.15x+0.29y=4.40. 15x+29y=440; 15x=440-29y... so y has to be a multiple of 5. at most y can be 5 or 10.(y=15 or greater would yield a negative number) y=5 doesnot give you a solution. y=10 is the only solution. From this X can be calculated. SUFFICIENT 11x +28y=440 Sufficient. 11x+20y=440 Sufficient. 11x +18y Not sufficient. (11x=440-18y. assuming y=11z, x=40-18z. so x could be 22 or 4). Re: A citrus fruit grower receives$15 for each crate of oranges   [#permalink] 12 Oct 2012, 20:20

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