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]

30 Nov 2009, 14:08

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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.

I rephrased this question to

15x + 29y = 440.

I understand how to get the solution of x=10, y=10. My question is how do I recognize that 15x+29y = 440 has 1 solution(x=10,y=10). When I first saw this problem I assumed that since I didn't have another equation in terms of x and y I couldn't solve for x and y since I didn't have 2 equations for 2 unknowns. I am just wondering if I see this on the GMAT then how I would recognize to go ahead with trying to find 1 solution.

Thanks.

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Re: OG 12 DS 123 Help [#permalink]

30 Nov 2009, 14:43

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.

I rephrased this question to

15x + 29y = 440.

I think its just trial and error and applying all your knowledge of math...

for eg., we know that she bought .15 and .29 stamps and no other denominations.

so is there a combination that gives 4.40 from .15 and .29 , yes 10 and 10; we have to make sure that there is no other solution to get to 4.40 using .15 and .29

if we try 11 for 0.15 then it is 1.65 and the rest 2.75 is not a multiple of 0.29 , so must not be 11 0.15 stamps.

15x +29y=440, we know x and y are atleast 1
lets try
x=1 then y must be (440-15)/29 and the result is not an integer so x must not be 1
trying in this we we only find x=10 and y=10 to be a solution and other combinations dont work.... hence it has to be x=y=10

I am sorry, I too dont have a better way to answer this..Well I just tried...

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Re: OG 12 DS 123 Help [#permalink]

30 Nov 2009, 14:52

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JimmyWorld wrote:

My quick way,

15x will end in a 5 or 0 so 29y must end in a 0 or 5 as well to get 440. That means y has to be 5 or 10.

Testing both only 10 will work

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Re: OG 12 DS 123 Help [#permalink]

16 Apr 2011, 04:36

Quote:

JimmyWorld 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.

I rephrased this question to

15x + 29y = 440.

I understand how to get the solution of x=10, y=10. My question is how do I recognize that 15x+29y = 440 has 1 solution(x=10,y=10). When I first saw this problem I assumed that since I didn't have another equation in terms of x and y I couldn't solve for x and y since I didn't have 2 equations for 2 unknowns. I am just wondering if I see this on the GMAT then how I would recognize to go ahead with trying to find 1 solution.

Thanks.

My quick way,

15x will end in a 5 or 0 so 29y must end in a 0 or 5 as well to get 440. That means y has to be 5 or 10.

Testing both only 10 will work

Dang, I should've seen this! Props!

Re: OG 12 DS 123 Help [#permalink] 16 Apr 2011, 04:36

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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

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

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