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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]  30 Nov 2009, 13:08
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Question Stats:

57% (01:40) correct 43% (00:51) wrong based on 81 sessions
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.

[Reveal] Spoiler:
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Dec 2013, 00:37, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: OG 12 DS 123 Help [#permalink]  30 Nov 2009, 13:43
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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 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, 13:52
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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
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Re: OG 12 DS 123 Help [#permalink]  16 Apr 2011, 03:36
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!
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Re: Joanna bought only $0.15 stamps and$0.29 stamps. How many [#permalink]  24 Dec 2013, 07:20
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Re: Joanna bought only $0.15 stamps and$0.29 stamps. How many [#permalink]  24 Dec 2013, 08:43
JimmyWorld wrote:
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).

lagomez 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

Although it is a neat method I would keep it up my sleeve as a bailout method. It really depends on the equation the gmat faces you with. If the equation had been 9x+14y=206 the unit digit combination would have been slightly more time consuming figure out. In my opionion use brute force "testing numbers" as a first option -as far as I have noticed the gmat wants to acknowledge if you are able to spot that the equation yields a unic solution and thus testing few numbers you will find your answer very quickly- but train your eye to recognize cases such as that one you pointed out and apply the unit digit trick. Lean towards the test, if you have two weapons you want to select the one that slays your foe faster

Hope it helps.
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Re: Joanna bought only $0.15 stamps and$0.29 stamps. How many [#permalink]  25 Dec 2013, 00:38
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Expert's post
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html
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Re: Joanna bought only $0.15 stamps and$0.29 stamps. How many [#permalink]  25 Dec 2013, 00:38
Expert's post
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html

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
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joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html
at-an-amusement-park-tom-bought-a-number-of-red-tokens-and-126814.html
collections-confused-need-a-help-81062.html
martha-bought-several-pencils-if-each-pencil-was-either-a-86509.html

Hope this helps.
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Re: Joanna bought only $0.15 stamps and$0.29 stamps. How many   [#permalink] 25 Dec 2013, 00:38
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