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Joanna bought only $0.15 stamps and $0.29 stamps. How many

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Joanna bought only $0.15 stamps and $0.29 stamps. How many [#permalink] New post 28 Jul 2010, 05:49
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Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy ?
1 she bought $4.40 worth of stamps
2 She bought an equal number of $0.15 stamps and 0.29 stamps .

I was thinking we need the total stamps as an addtional information so I picked E !

pleas help me understand
thanks
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Re: D.S [#permalink] New post 28 Jul 2010, 05:59
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xmagedo wrote:
Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy ?
1 she bought $4.40 worth of stamps
2 She bought an equal number of $0.15 stamps and 0.29 stamps .

I was thinking we need the total stamps as an addtional information so I picked E !

pleas help me understand
thanks


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 non-negative integers, there can be multiple solutions possible for x and y (eg 5x+6y=60) OR just one combination (eg 15x+29y=440). Hence in some cases ax+by=c is NOT sufficient and in some cases it is sufficient.

For more on this type of questions check: gmat-prep2-92785.html?hilit=stamps

Hope it helps.
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Re: D.S [#permalink] New post 29 Jul 2010, 01:44
Statement 1: equation 15x+29y=440
since both 15x and 440 are multiples of 5 then y=5, 10, 15, 20, ...
since 290y<440 then y<20 then y=5, 10, 15
since 15x mod 3 = 0, 29 mod 3 = 2, 440 mod 3 = 2, then y mod 3 = 1, or y=10
sufficient

Statement 2: clearly not sufficient

Notation: (a mod b) gives remainder when divide a by b
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Re: D.S   [#permalink] 29 Jul 2010, 01:44
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