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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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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

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

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03 Nov 2012, 22:37

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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 )

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!!"

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

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03 Nov 2012, 23:15

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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 )

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)

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

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." _________________

Yogi Bhajan: If you want to learn a thing, read that; if you want to know a thing, write that; if you want to master a thing, teach that. This message transmitted on 100% recycled electrons.

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

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."

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

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

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10 Jul 2015, 09:30

Expert's post

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. _________________

The only time you can lose is when you give up. Try hard and you will suceed. Thanks = Kudos. Kudos are appreciated

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

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10 Jul 2015, 14:35

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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.

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