• NEW! FREE Beat The GMAT Quizzes  Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Julie opened a lemonade stand and sold lemonade in two ##### This topic has 4 expert replies and 0 member replies ### Top Member ## Julie opened a lemonade stand and sold lemonade in two ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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

OA B

Source: Veritas Prep

### GMAT/MBA Expert

GMAT Instructor Joined
08 Dec 2008
Posted:
12733 messages
Followed by:
1246 members
5254
GMAT Score:
770
This question illustrates a common trap on the GMAT.

For statement 2, we're able to write the equation 52x + 58y = 492 , and in high school we learned that, if we're given 1 equation with 2 variables, we cannot find the value of either variable. However, if we restrict the variables to positive integers within a certain range of values, then there are times when we can find the value of a variable if we're given 1 equation with 2 variables.

Here's another question that exploits this common misconception: https://www.beatthegmat.com/stamps-t288085.html

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Sign up for our free Question of the Day emails
And check out all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

GMAT Instructor Joined
25 May 2010
Posted:
15186 messages
Followed by:
1860 members
13060
GMAT Score:
790
BTGmoderatorDC 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 Let X = the number of 52¢ lemonades and Y = the number of 58¢ lemonades. Since the question stem asks for the number of 52¢ lemonades, we get: What is the value of X? Statement 1: X+Y = 9 Since X can be any value between 0 and 9, inclusive, INSUFFICIENT. Statement 2: 52X + 58Y = 492 Since the two statements cannot contradict each other, an integral solution for the equation above must be yielded when X+Y=9. If a total of 9 lemonades are sold, the equation above implies the following: Average cost per lemonade = 492/9 ≈ 54.66. Since the average cost is just a bit closer to 52 than to 58, the number of 52¢ lemonades must be a just bit greater than the number of 58¢ lemonades, implying that X=5 and Y=4: 5*52 + 4*58 = 260 + 232 = 492. In the case above, X:Y = 5:4. Check whether OTHER revenue ratios are also possible. Since the lemonade values are 52¢ and 58¢, the revenue ratio can be altered only by adding a multiple of 52 and 58 to X or Y, while subtracting this multiple from the other variable. Since 52 = 2*26 and 58 = 2*29, the LCM of 52 and 58 = 2*26*29. If 2*26*29 is added to either 52¢ or 58¢, the sum will exceed 492¢. Thus, the revenue ratio CANNOT be altered, implying that only ONE revenue ratio will satisfy statement 2: X=5 and Y=4. Thus, X=5. SUFFICIENT. The correct answer is B. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1429 messages Followed by: 31 members Upvotes: 59 BTGmoderatorDC 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
Source: Veritas Prep
$$\left\{ \matrix{ \,m \ge 1\,\,{\mathop{\rm int}} \,\,\,12{\rm{oz - units}}\,\,,\,\,52\,{\rm{cents}}\,{\rm{each}} \hfill \cr \,n \ge 1\,\,{\mathop{\rm int}} \,\,\,\,16{\rm{oz - units}}\,\,,\,\,58\,{\rm{cents}}\,{\rm{each}}\,\,\, \hfill \cr} \right.\,\,\,\,\left( * \right)$$
$$? = m$$
$$\left( 1 \right)\,\,m + n = 9\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {1,8} \right)\,\,\,\, \Rightarrow \,\,\,? = 1\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,7} \right)\,\,\,\, \Rightarrow \,\,\,? = 2\,\, \hfill \cr} \right.$$

Money unit will be CENTS. (All amounts in cents are integers!)
$$\left( 2 \right)\,\,52m + 58n = 492\,\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,2} \,\,\,\,\,26m + 29n = 246\,\,\,$$
$$\left[ {29n\,\,\mathop = \limits^{\left( * \right)} \,} \right]\,\,{\rm{positive}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,29\,\, = \,\,\,246 - 26m = 2\left( {123 - 13m} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{GCF}}\,\left( {2,29} \right)\,\, = \,\,1} \,\,\,123 - 13m\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{positive}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,29$$
$\left. \begin{gathered} m = 1\,\,\,\, \Rightarrow \,\,\,123 - 13 = 110\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ m = 2\,\,\,\, \Rightarrow \,\,\,123 - 26 = 97\,\,\left[ { = 110 - 13} \right]\,\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ m = 3\,\,\,\, \Rightarrow \,\,\,123 - 39 = 84\,\,\left[ { = 97 - 13} \right]\,\,\,\,\,\,\left( {{\text{NO}}} \right)\,\,\,\, \hfill \\ m = 4\,\,\,\, \Rightarrow \,\,\,84 - 13 = 71\,\,\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ \boxed{m = 5}\,\,\,\, \Rightarrow \,\,\,71 - 13 = 58 = 2 \cdot 29\,\,\,\,\,\left( {{\text{YES}}} \right)\,\,\,\,\,\,\,\,\,\,\, \hfill \\ m = 6\,\,\,\, \Rightarrow \,\,\,58 - 13 = 45\,\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ m = 7\,\,\,\, \Rightarrow \,\,\,45 - 13 = 32\,\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ m = 8\,\,\,\, \Rightarrow \,\,\,32 - 13 = 19\,\,\,\,\,\left( {{\text{NO}}} \right) \hfill \\ \end{gathered} \right\}\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = 5$

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

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert

GMAT Instructor Joined
22 Aug 2016
Posted:
1817 messages
Followed by:
29 members
470
BTGmoderatorDC 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 OA B Source: Veritas Prep Given: Julie sells lemonade in two different sizes, a 52-cent (12oz) and a 58-cent (16oz) size Question: How many 52-cent (12oz) lemonade drinks did Julie sell? Let's take each statement one by one. (1) Julie sold a total of 9 lemonades. Certainly insufficient. (2) The total value of the lemonade drinks Julie sold was$4.92.

Say, the number of 12oz lemonades sold is x and the number of 16oz lemonades sold is y.

Then, 52x + 58y = 492

=> 26x + 29y = 246

x = (246 - 29y)/26

= 9 + (12 - 29y)/26

= 9 + (12 - 26y - 3y)/26

= 9 + (12 - 3y)/26 - 26y/26

= 9 + (12 - 3y)/26 - y

Since x is a positive integer, (12 - 3y) must be a multiple of 26.

Let's try some values for y to make (12 - 3y) must be a multiple of 26.

@y = 4, we have (12 - 3y) => 12 - 3*4 = 12 - 12 = 0 -- a multiple of 26.

Thus, x = 9 + 0 - 4 = 5.

We must try a few more values for y so that (12 - 3y) must be a multiple of 26 and x is a positive integer.

Note that at higher values of y, the term [(12 - 3y)/26 - y] would be negative, making x a negative integer, which is an invalid value. You'll find that there is no another possible valid value of y. Thus, y = 4 and y = 5. Sufficient.

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangalore | Guangzhou | Buenos Aires | and many more...

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

### Top First Responders*

1 GMATGuruNY 58 first replies
2 Jay@ManhattanReview 53 first replies
3 Brent@GMATPrepNow 47 first replies
4 Ian Stewart 23 first replies
5 ceilidh.erickson 12 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

188 posts
2 fskilnik@GMATH

GMATH Teacher

154 posts
3 Max@Math Revolution

Math Revolution

91 posts
4 GMATGuruNY

The Princeton Review Teacher

83 posts
5 Brent@GMATPrepNow

GMAT Prep Now Teacher

76 posts
See More Top Beat The GMAT Experts