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Julie opened a lemonade stand and sold lemonade in two diff

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Julie opened a lemonade stand and sold lemonade in two diff [#permalink] New post 03 Nov 2012, 21:23
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Julie opened a lemonade stand and sold lemonade in two different sizes, a 52-cent (12oz) and a 58-cent (16oz) size. How many 52-cent (12oz) lemonade drinks did Julie sell?

(1) Julie sold a total of 9 lemonades
(2) The total value of the lemonade drinks Julie sold was $4.92
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Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] New post 03 Nov 2012, 21:37
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tim415 wrote:
Julie opened a lemonade stand and sold lemonade in two different sizes, a 52-cent (12oz) and a 58-cent (16oz) size. How many 52-cent (12oz) lemonade drinks did Julie sell?

(1) Julie sold a total of 9 lemonades
(2) The total value of the lemonade drinks Julie sold was $4.92


Cost of 12 oz drink =52 cents, lets assumte total number sold are N
Cost of 16 oz drink =58 cents, lets assumte total number sold are M

Statement 1: N+M =9
So it could be that N=1, M=8 or that N=2, M=7 etc. Clearly not sufficient.

Statement 2: N*0.52 + M*0.58 = 4.92
Or to simplify it: N*52 + M*58 = 492
N*26 + M*29 = 246
M*29 = 246-N*26
This is true only for one value of M and N, when M=4 and N=5. (Assuming number of drinks to be only integers and hoping Julie's stand is not a unique stand that sells 0.732, 0.981 drinks :P )

Hence sufficient to answer.

Ans B it is.
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Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] New post 03 Nov 2012, 22:15
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tim415 wrote:
Vips0000 wrote:
M*29 = 246-N*26
This is true only for one value of M and N, when M=4 and N=5. (Assuming number of drinks to be only integers and hoping Julie's stand is not a unique stand that sells 0.732, 0.981 drinks :P )



Thanks! Hmm.. I think I'm missing something pretty obvious here, how do you conclude that there is only one value for M and N and that it has to be M=4, N=5? When I look at the equation I see 1 equation and 2 unknowns so my knee jerk reaction is "not solvable!!" :?


Well, when question or context gives you certain constraints to help you. (Or actually to trick you :P )

If we dont know that number of drinks got to be a non-negative integer then surely we can not solve 1 equation with 2 variables. But in this case that is one underlying constraint. So we can simply check if there is anything that satisifies the equation.

Remember this trick for any such context (Number of drinks/ animals/ trees/ votes/ persons etc)

Hope it helps :)
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Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] New post 06 Nov 2012, 04:16
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tim415 wrote:
Julie opened a lemonade stand and sold lemonade in two different sizes, a 52-cent (12oz) and a 58-cent (16oz) size. How many 52-cent (12oz) lemonade drinks did Julie sell?

(1) Julie sold a total of 9 lemonades
(2) The total value of the lemonade drinks Julie sold was $4.92


Similar questions to practice:
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
common-gmat-trap-31x-25y-128578.html

Hope it helps.
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Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] New post 03 Nov 2012, 22:09
Vips0000 wrote:
M*29 = 246-N*26
This is true only for one value of M and N, when M=4 and N=5. (Assuming number of drinks to be only integers and hoping Julie's stand is not a unique stand that sells 0.732, 0.981 drinks :P )



Thanks! Hmm.. I think I'm missing something pretty obvious here, how do you conclude that there is only one value for M and N and that it has to be M=4, N=5? When I look at the equation I see 1 equation and 2 unknowns so my knee jerk reaction is "not solvable!!" :?
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Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] New post 15 Jul 2013, 19:36
Vips0000 wrote:
tim415 wrote:
Vips0000 wrote:
M*29 = 246-N*26
This is true only for one value of M and N, when M=4 and N=5. (Assuming number of drinks to be only integers and hoping Julie's stand is not a unique stand that sells 0.732, 0.981 drinks :P )



Thanks! Hmm.. I think I'm missing something pretty obvious here, how do you conclude that there is only one value for M and N and that it has to be M=4, N=5? When I look at the equation I see 1 equation and 2 unknowns so my knee jerk reaction is "not solvable!!" :?


Well, when question or context gives you certain constraints to help you. (Or actually to trick you :P )

If we dont know that number of drinks got to be a non-negative integer then surely we can not solve 1 equation with 2 variables. But in this case that is one underlying constraint. So we can simply check if there is anything that satisifies the equation.

Remember this trick for any such context (Number of drinks/ animals/ trees/ votes/ persons etc)

Hope it helps :)


Can you please explain the statement again ? I got the answer choice wrong. "If we dont know that number of drinks got to be a non-negative integer then surely we can not solve 1 equation with 2 variables. But in this case that is one underlying constraint. So we can simply check if there is anything that satisifies the equation."
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Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] New post 15 Jul 2013, 21:41
Expert's post
hb wrote:
Vips0000 wrote:
tim415 wrote:


Thanks! Hmm.. I think I'm missing something pretty obvious here, how do you conclude that there is only one value for M and N and that it has to be M=4, N=5? When I look at the equation I see 1 equation and 2 unknowns so my knee jerk reaction is "not solvable!!" :?


Well, when question or context gives you certain constraints to help you. (Or actually to trick you :P )

If we dont know that number of drinks got to be a non-negative integer then surely we can not solve 1 equation with 2 variables. But in this case that is one underlying constraint. So we can simply check if there is anything that satisifies the equation.

Remember this trick for any such context (Number of drinks/ animals/ trees/ votes/ persons etc)

Hope it helps :)


Can you please explain the statement again ? I got the answer choice wrong. "If we dont know that number of drinks got to be a non-negative integer then surely we can not solve 1 equation with 2 variables. But in this case that is one underlying constraint. So we can simply check if there is anything that satisifies the equation."


Check these posts:
joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html
common-gmat-trap-31x-25y-128578.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
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

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Julie opened a lemonade stand and sold lemonade in two diff   [#permalink] 15 Jul 2013, 21:41
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