GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Jan 2019, 15:16

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
• Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

Author Message
TAGS:

Hide Tags

Intern
Joined: 07 Oct 2012
Posts: 14

Show Tags

03 Nov 2012, 21:23
1
5
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:17) correct 31% (01:05) wrong based on 368 sessions

HideShow timer Statistics

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 Most Helpful Community Reply Director Status: Done with formalities.. and back.. Joined: 15 Sep 2012 Posts: 587 Location: India Concentration: Strategy, General Management Schools: Olin - Wash U - Class of 2015 WE: Information Technology (Computer Software) Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] Show Tags 03 Nov 2012, 21:37 4 1 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 )

Ans B it is.
_________________

Lets Kudos!!!
Black Friday Debrief

General Discussion
Intern
Joined: 07 Oct 2012
Posts: 14

Show Tags

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 )

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!!"
Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 587
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)

Show Tags

03 Nov 2012, 22:15
1
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
_________________

Lets Kudos!!!
Black Friday Debrief

Math Expert
Joined: 02 Sep 2009
Posts: 52390

Show Tags

06 Nov 2012, 04:16
1
3
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. _________________ Intern Status: Yes. It was I who let the dogs out. Joined: 03 Dec 2012 Posts: 38 Location: Canada H: B Concentration: General Management, Leadership GMAT Date: 08-31-2013 Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] Show Tags 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 ) 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. Math Expert Joined: 02 Sep 2009 Posts: 52390 Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] Show Tags 15 Jul 2013, 21:41 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. _________________ Director Joined: 23 Jan 2013 Posts: 560 Schools: Cambridge'16 Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] Show Tags 04 Nov 2014, 21:17 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 Retired Moderator Joined: 18 Sep 2014 Posts: 1112 Location: India Julie opened a lemonade stand and sold lemonade in two diff [#permalink] Show Tags 10 Jul 2015, 08:30 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 )

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.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13375
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170

Show Tags

10 Jul 2015, 13:35
1
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 Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Manager Joined: 01 Jun 2015 Posts: 215 Location: India Concentration: Strategy, International Business GMAT 1: 620 Q48 V26 Julie opened a lemonade stand and sold lemonade in two diff [#permalink] Show Tags 25 Feb 2018, 05:40 VeritasPrepKarishma how to conclude that there is only one value for M and N for the equation M*29 = 246-N*26 Please help. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13375 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Julie opened a lemonade stand and sold lemonade in two diff [#permalink] Show Tags 25 Feb 2018, 14:24 1 techiesam wrote: VeritasPrepKarishma how to conclude that there is only one value for M and N for the equation M*29 = 246-N*26 Please help. Hi techiesam, If you read my explanation (the post that immediately appears before your post), you'll see that with a little logic - and some 'brute force' arithmetic - you can prove that there's only one solution when you include the information in Fact 2. 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 Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Manager
Joined: 01 Jun 2015
Posts: 215
Location: India
GMAT 1: 620 Q48 V26

Show Tags

25 Feb 2018, 21:03
EMPOWERgmatRichC wrote:
techiesam wrote:
VeritasPrepKarishma

how to conclude that there is only one value for M and N for the equation M*29 = 246-N*26

Hi techiesam,

If you read my explanation (the post that immediately appears before your post), you'll see that with a little logic - and some 'brute force' arithmetic - you can prove that there's only one solution when you include the information in Fact 2.

GMAT assassins aren't born, they're made,
Rich

Thanks..But the brute force method is time consuming,specially when you are taking the test.Is there any other way!
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8805
Location: Pune, India

Show Tags

25 Feb 2018, 21:24
techiesam wrote:
VeritasPrepKarishma

how to conclude that there is only one value for M and N for the equation M*29 = 246-N*26

Check out this post: https://www.veritasprep.com/blog/2011/0 ... -of-thumb/

It discusses in detail how to solve equations with integer solutions and also how you can find out the exact number of solutions an equation such as this will have.
_________________

Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 01 Jun 2015
Posts: 215
Location: India
GMAT 1: 620 Q48 V26

Show Tags

25 Feb 2018, 21:32
VeritasPrepKarishma wrote:
techiesam wrote:
VeritasPrepKarishma

how to conclude that there is only one value for M and N for the equation M*29 = 246-N*26

Check out this post: https://www.veritasprep.com/blog/2011/0 ... -of-thumb/

It discusses in detail how to solve equations with integer solutions and also how you can find out the exact number of solutions an equation such as this will have.

Thank you very much Ma'am.This is what I've been looking for.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 629

Show Tags

08 Oct 2018, 11:07
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

$$\left\{ \begin{gathered} \,m \geqslant 1\,\,\operatorname{int} \,\,\,12{\text{oz - units}}\,\,,\,\,52\,{\text{cents}}\,{\text{each}} \hfill \\ \,n \geqslant 1\,\,\operatorname{int} \,\,\,\,16{\text{oz - units}}\,\,,\,\,58\,{\text{cents}}\,{\text{each}}\,\,\, \hfill \\ \end{gathered} \right.\,\,\,\,\left( * \right)$$

$$? = m$$

$$\left( 1 \right)\,\,m + n = 9\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {m,n} \right) = \left( {1,8} \right)\,\,\,\, \Rightarrow \,\,\,? = 1\,\, \hfill \\ \,{\text{Take}}\,\,\left( {m,n} \right) = \left( {2,7} \right)\,\,\,\, \Rightarrow \,\,\,? = 2\,\, \hfill \\ \end{gathered} \right.$$

Money unit will be CENTS. (All amounts in cents are integers!)

$$\left( 2 \right)\,\,52m + 58n = 492\,\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,2} \,\,\,\,\,26m + 29n = 246\,\,\,$$

$$\left[ {29n\,\,\mathop = \limits^{\left( * \right)} \,} \right]\,\,{\text{positive}}\,\,{\text{multiple}}\,\,{\text{of}}\,\,29\,\, = \,\,\,246 - 26m = 2\left( {123 - 13m} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{GCF}}\,\left( {2,29} \right)\,\, = \,\,1} \,\,\,123 - 13m\,\,{\text{is}}\,\,{\text{a}}\,\,{\text{positive}}\,\,{\text{multiple}}\,\,{\text{of}}\,\,29$$

$$\left. \begin{gathered} m = 1\,\,\,\, \Rightarrow \,\,\,123 - 13 = 110\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ m = 2\,\,\,\, \Rightarrow \,\,\,123 - 26 = 97\,\,\left[ { = 110 - 13} \right]\,\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ m = 3\,\,\,\, \Rightarrow \,\,\,123 - 39 = 84\,\,\left[ { = 97 - 13} \right]\,\,\,\,\,\,\left( {{\text{NO}}} \right)\,\,\,\, \hfill \\ m = 4\,\,\,\, \Rightarrow \,\,\,84 - 13 = 71\,\,\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ \boxed{m = 5}\,\,\,\, \Rightarrow \,\,\,71 - 13 = 58 = 2 \cdot 29\,\,\,\,\,\left( {{\text{YES}}} \right)\,\,\,\,\,\,\,\,\,\,\, \hfill \\ m = 6\,\,\,\, \Rightarrow \,\,\,58 - 13 = 45\,\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ m = 7\,\,\,\, \Rightarrow \,\,\,45 - 13 = 32\,\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ m = 8\,\,\,\, \Rightarrow \,\,\,32 - 13 = 19\,\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ \end{gathered} \right\}\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = 5$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Re: Julie opened a lemonade stand and sold lemonade in two diff &nbs [#permalink] 08 Oct 2018, 11:07
Display posts from previous: Sort by