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A citrus fruit grower receives $15 for each crate of oranges

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Re: Gmat prep2 [#permalink] New post 21 Apr 2012, 09:45
Expert's post
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.

Answer: A.

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] New post 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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