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Register now and save up to $200 Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code ## #60 Official Guide This topic has 4 expert replies and 0 member replies RahilM824 Newbie | Next Rank: 10 Posts Joined 02 Feb 2015 Posted: 1 messages #### #60 Official Guide Mon Feb 02, 2015 8:19 am Struggling with this one: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at$.60 a glass on the first day, what was the price per glass on the second day?

A) $.15 B)$.20
C) $.30 D)$.40
E) $.45 ### GMAT/MBA Expert Jeff@TargetTestPrep GMAT Instructor Joined 09 Apr 2015 Posted: 877 messages Followed by: 12 members Upvotes: 39 Fri May 01, 2015 9:30 am RahilM824 wrote: Struggling with this one: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at$.60 a glass on the first day, what was the price per glass on the second day?

A) $.15 B)$.20
C) $.30 D)$.40
E) $.45 We are given that orangeade is made on Day 1 with an EQUAL AMOUNT of water and orange juice. We can set this information up into a ratio using a variable multiplier: W : OJ = x : x Thus, orangeade quantity = amount of water + amount of OJ = x + x = 2x We are next given that orangeade on Day 2 was made by mixing the SAME AMOUNT of orange juice with TWICE THE AMOUNT of water. We can set this information up into a ratio using a variable multiplier: W : OJ = 2x : x Thus, orangeade quantity = amount of water + amount of OJ = 2x + x = 3x We also know that all orangeade made was sold and that the revenue on both days was the same. We can therefore set up the following equation: Day 1 Revenue = Day 2 Revenue That is, (quantity sold Day 1)(price per glass Day 1) = (quantity sold Day 2)(price per glass Day 2) Let a be the amount of orangeade a glass can hold, then quantity sold Day 1 = the number of glasses of orangeade sold on Day 1 = 2x/a Similarly, quantity sold Day 2 = the number of glasses of orangeade sold on Day 2 = 3x/a We also know that the price per glass on day 1 =$0.6

But we donâ€™t know the price per glass on day 2, so letâ€™s label it as variable p.

We now have:

(2x/a)(0.6) = (3x/a)(p)

Multiplying both sides by a, we have:

(2x)(0.6) = (3x)(p)

1.2x = 3xp

1.2 = 3p

p = 0.4

Thus, each glass of orangeade was sold for $0.40 on Day 2. The answer is D _________________ Jeffrey Miller Head of GMAT Instruction ### GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 14031 messages Followed by: 1812 members Upvotes: 13060 GMAT Score: 790 Mon Feb 02, 2015 9:37 am RahilM824 wrote: Struggling with this one: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at$.60 a glass on the first day, what was the price per glass on the second day?

A) $.15 B)$.20
C) $.30 D)$.40
E) $.45 First day: Here, equal amounts of juice and water are used. Let amount of orangeade = 1 glass juice + 1 glass water = 2 glasses. Since each glass earns 60 cents, revenue = 2*60 = 120 cents. Second day: Revenue = 120 cents (same as on the first day). Since twice as much water is used, amount of orangeade = 1 glass juice + 2 glasses water = 3 glasses. Price per glass = revenue/glasses = 120/3 = 40 cents. The correct answer is D. _________________ Mitch Hunt GMAT Private Tutor 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. 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 DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 120 members Upvotes: 1153 GMAT Score: 770 Mon Feb 02, 2015 8:24 am Initially, you have a certain amount of orangeade and the same amount of water. So let's call each 'x.' Water: x Orangeade: x Total: 2x Well, let's say that this 2x volume of juice translates to 100 servings. (I'm picking this number simply because it's nice and round. Any number will work.) Well my total revenue will be 100 * .60 = 60 The next day we're doubling the water, so we'll have Water: 2x Orangeade: x Total: 3x Note that we have 50% more juice volume, because 3x is 50% greater than 2x. So now, if we initially had 100 servings, we'll have 150 servings. The revenue remains the same so we need to solve for the price, giving us the following equation: 150 * P = 60 P = 60/150 = .40. Answer is D. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

DavidG@VeritasPrep Legendary Member
Joined
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Posted:
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Followed by:
120 members
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GMAT Score:
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Mon Feb 02, 2015 8:28 am
Also note that anytime we're working with the following equation: quantity*price = revenue, if we hold the revenue constant, price and quantity will have an inverse relationship. In other words, if the price is doubled, the quantity will be halved, etc. In this case, we're multiplying the quantity by 3/2, which means that if we're holding the revenue constant, we'd need to multiply the price by 2/3. .60 *2/3 = .40.

[And the same logic would apply to the relationship between rate and time if we hold distance constant, so this is a useful piece of logic that can be applied in multiple domains.]

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