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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]

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03 Nov 2012, 22:23
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Question Stats:

66% (02:13) correct 34% (00:59) wrong based on 223 sessions

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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 [Reveal] Spoiler: OA Director Status: Done with formalities.. and back.. Joined: 15 Sep 2012 Posts: 641 Location: India Concentration: Strategy, General Management Schools: Olin - Wash U - Class of 2015 WE: Information Technology (Computer Software) Followers: 49 Kudos [?]: 589 [3] , given: 23 Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] ### Show Tags 03 Nov 2012, 22:37 3 This post received KUDOS 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 )

Hence sufficient to answer.

Ans B it is.
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Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
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Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink]

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03 Nov 2012, 23:15
1
KUDOS
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 )

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 )

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]

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06 Nov 2012, 05:16
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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. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9122 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 445 Kudos [?]: 2874 [1] , given: 169 Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] ### Show Tags 10 Jul 2015, 14:35 1 This post received KUDOS Expert's post Hi Mechmeera, In situations such as this (when you THINK that you need two variables and two unique equations to answer the given question), it helps to be on the lookout for "weird" numbers and/or low "totals." You also have to be ready to do some 'brute force' work to get the solution. In this prompt, we're told that the two sizes cost 52 cents and 58 cents. Fact 2 tells us that the TOTAL value of glasses sold was$4.92. Since each size of lemonade sells for OVER 50 cents, and the total is LESS than $5, there must be FEWER than 10 lemonades sold - this leads to a relatively small number of possibilities. While the work might seem a little tedious, you CAN list out the various 'multiples' of each size and look for an option that totals$4.92

For the 12-ounce lemonade:
.52
1.04
1.56
2.08
2.60
3.12
3.64
4.16
4.68

For the 16-ounce lemonade:
.58
1.16
1.74
2.32
2.90
3.48
4.06
4.64

How many ways are there to add a number from the first group to the number from the second group and get a TOTAL of $4.92 (hint: the units digit is a '2', so look for a pair of values that SUM to that units digit). You'll find that there's just one pairing. Thus, Fact 2 is SUFFICIENT. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Intern
Joined: 07 Oct 2012
Posts: 14
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Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink]

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03 Nov 2012, 23:09
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 )

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]

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15 Jul 2013, 20:36
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 )

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 )

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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Math Expert
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Kudos [?]: 106329 [0], given: 11621

Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink]

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15 Jul 2013, 22:41
Expert's post
1
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BOOKMARKED
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 )

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.
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Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink]

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04 Nov 2014, 22:17
This is Value type of DS questions in which we should answer if there is only one value or more than one value.
If only one possible value - sufficient
If more than one value - insufficient

We do not need to count this value as we do in PS

In this case we should answer if it is only one possible value of 52-cent lemonade drinks' number

S1. x+y=9, can be 1+8, 2+7, 3+6, 4+5..., so INSUFFICIENT
S2. 52x+58y=492, we have two different prices per drink, so there is always unique number of X (non-negative integer), so SUFFICIENT

B
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Julie opened a lemonade stand and sold lemonade in two diff [#permalink]

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10 Jul 2015, 09:30
Vips0000 wrote:
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 )

Hence sufficient to answer.

Ans B it is.

It took a lot of time for me to arrive at the values.
I agree this is a DS question and solving till the last line is not required as in case of PS.
but still the equation looks quite complex that I felt it may not have a solution at all.
Is there is any way to solve the equation in less time.
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Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink]

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28 Oct 2016, 05:41
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Re: Julie opened a lemonade stand and sold lemonade in two diff   [#permalink] 28 Oct 2016, 05:41
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# Julie opened a lemonade stand and sold lemonade in two diff

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