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# On a certain day, orangeade was made by mixing a certain

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08 Oct 2012, 01:01
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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 $0.60 per glass on the first day, what was the price per glass on the second day? (A)$015
(B) $0.20 (C)$0.30
(D) $0.40 (E)$0.45

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08 Oct 2012, 01:02
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SOLUTION

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 $0.60 per glass on the first day, what was the price per glass on the second day? (A)$015
(B) $0.20 (C)$0.30
(D) $0.40 (E)$0.45

On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;

So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.

We are told that "the revenue from selling the orangeade was the same for both days" so the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.

Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4.

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08 Oct 2012, 02:07
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It is better to take smart numbers rather than getting confused in ratio's.
So lets say on Day1 = 10 liters was sold ( Orange :Water, 5:5 lt) [1 glass = 1liter]
So Revenue on Day1 = 10 * 0.6

Ratio on 2nd day ( Orange :Water, 5:10 lt) 15 lt = 15 glassess
Day1 revenue = Day2 revenue
10 * 0.6 = 15 *x
x = 0.4
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Updated on: 08 Oct 2012, 02:33
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Lets say on 1st day we can make 2 glasses of mixture with 1:1 ratio, There fore cost of 2 glasses of juice = 2 X .60
On the second day we will have 3 glasses of juice since we are mixing in a 1:2 ratio. Cost = 3 X P (P=cost per glass)

Since revenue is same we can equate both cost, ie 2X .60 = 3 X P => P = .40
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Originally posted by SOURH7WK on 08 Oct 2012, 01:45.
Last edited by SOURH7WK on 08 Oct 2012, 02:33, edited 1 time in total.
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08 Oct 2012, 02:41
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Lets say two glasses (one glass juice + one glass water) were sold on the first day at 0.6$per glass. Revenue on first day = 1.2$
So, revenue on second day = 1.2$Three glass (one glass juice + 2 glasses water) were sold on second day. So, price per glass = 1.2/3 = 0.40$
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08 Oct 2012, 08:58
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What a big misktake i was actually doing ..i was just assuming ..that if its .60 on first day..then .30 will be on second because of addding twwice water..

after luking at above solution ..i change took D too :D

well

10 +10=20 *.60=12

10 is orange juice and 10 litre water...

10+20=30..

10 is orange...20 litter is water ...as mentioned twice the amount..

12=30*x

12/30=4/10=.40=D=ans=:)
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09 Oct 2012, 22:48
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Since solution by picking numbers is already given by many, hence to add to it the algebric solution is given below:

Assume volume of Orange and water added on first day is each V.
Hence total orangeade on day 1=V+V = 2V

On day 2, volume of water is doubled,
Hence total orangeade on day 2 = V + 2V = 3V

Assume, volume of 1 glass = G

For given question, if reveneue on Day 1 and Day 2 are same that would mean:

2 V * P1/ G = 3V *P2/G,
where P1 and P2 are price per glass on Day1 and Day2 respectively.

=> P2 = 2/3 *P1
We have P1 = 0.60 hence, P2 = 2/3*0.60 = 0.40

Ans D

Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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 $0.60 per glass on the first day, what was the price per glass on the second day? (A)$015
(B) $0.20 (C)$0.30
(D) $0.40 (E)$0.45

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10 Jan 2014, 00:18
For the first day, we are given: X*(OJ) + X*(W) = Orangeade ----> For each glass, X accounts for 2 units

For the second day we are given X*(OJ) + 2X*(W) = Orangeade -----> For each glass, X accounts for 3 units

If, for 2 X, the "per unit" price is 0.3 (0.6/2), then for 3 X, the "per unit" price is 0.2 (0.6/3) ---> subtract the difference from the original: 0.6 - 0.2 = 0.4

The reason we subtract the difference is because we are told that the revenue is the same for both days.

Thus, the difference in per-glass revenue is equal to subtracting 0.2 from each sale because our 3/2 units of X in day two compared to day one dilutes our "per unit of X" revenue. So, when we know the magnitute of dilution, we know the cost of a glass in day 2.
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10 Jan 2014, 01:04
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Let total orangeade on first day be 2x units.

R1=2x*.60=1.20x
R2=3x*T(say)

R1=R2
T=1.20x/3x=.40 per glass

Ans. D
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11 Jun 2014, 03:20
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On the 2nd the amount sold was greater 1/3 than on the 1st day --> So the price should be 1/3 lower then 0,60
0,60x2/3 = 40
or one paid 0,60 for 1 liter mix on the 1st day -> the Volume got 1/3 greater - 1,5X = 60 ; X = 40

Update 2015
It's a proportion here R = Glases*Price if we raise the # of glases by 3/2 our price should change by 2/3 to keep the revenue unchanged (in balance or equal to the revenue of the 1st day) --> 0,60*2/3=0,40
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Schools: Tulane '18 (M$) Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 02 May 2016, 13:28 Simple question here, hoping this helps anyone! OJ + W = D1 OJ + 2W = D2 1 part OJ + 1 part W = 2 parts * .6 = 1.20 1 part OJ + 2 part W = 3 parts * x = 1.20 3 parts * x = 1.20 1.20 / 3 = x = .4 VP Joined: 07 Dec 2014 Posts: 1150 On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags Updated on: 21 Dec 2018, 16:57 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$0.60 per glass on the first day, what was the price per glass on the second day?

(A) $015 (B)$0.20
(C) $0.30 (D)$0.40
(E) $0.45 let x=price per glass on second day x/(1/3)=60¢/(1/2) x=40¢ D Originally posted by gracie on 03 May 2016, 19:34. Last edited by gracie on 21 Dec 2018, 16:57, edited 1 time in total. Manager Joined: 20 Jun 2013 Posts: 52 Location: India Concentration: Economics, Finance GMAT 1: 430 Q39 V25 GPA: 3.5 WE: Information Technology (Other) Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 20 Apr 2017, 14:49 good one... thanks.... i by mistake counted half and marked it 0.3.............. idiot...... thanks for a great question and a clearly expressed explaination by all ... thanks again Director Joined: 02 Sep 2016 Posts: 678 Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 08 Sep 2017, 05:27 1 First day: a + a= 2a Total revenue= 0.60*2a Second day: a+2a= 3a Let revenue = x 0.60*2a= x*3a x= 0.40 _________________ Help me make my explanation better by providing a logical feedback. If you liked the post, HIT KUDOS !! Don't quit.............Do it. Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4518 Location: United States (CA) Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 11 Sep 2017, 14:53 1 Bunuel wrote: 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$0.60 per glass on the first day, what was the price per glass on the second day?

(A) $015 (B)$0.20
(C) $0.30 (D)$0.40
(E) $0.45 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 as a ratio using a variable multiplier: W : OJ = x : x Thus, amount of orangeade = amount of water + amount of OJ = x + x = 2x. We are next given that orangeade is made on Day 2 by mixing the SAME AMOUNT of orange juice with TWICE THE AMOUNT of water. Again, we can set this information up as a ratio using a variable multiplier: W : OJ = 2x : x Thus, amount of orangeade = 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) We also know that the price per glass on Day 1 =$0.6

But we don’t know the price per glass on Day 2, so let’s label it as variable p.

We now 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. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8787 Location: Pune, India Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 18 Dec 2017, 04:40 Bunuel wrote: 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$0.60 per glass on the first day, what was the price per glass on the second day?

(A) $015 (B)$0.20
(C) $0.30 (D)$0.40
(E) $0.45 Practice Questions Question: 60 Page: 160 Difficulty: 650 Check out our video solution to this problem here: https://www.veritasprep.com/gmat-soluti ... olving_208 _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Intern Joined: 16 Jul 2016 Posts: 34 On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 18 Dec 2017, 08:33 (price/glass) * Glasses = revenue .6 (2x) = 1.2x (price/glass) (3x) = 1.2x So we assumed 2x glasses were sold on day 1. That means x glasses or orangeaide were used. For the next day 1/3 of each glass is orangeaide so there needs to be 3x glasses sold. $$(1.2x)/3x=.4$$ whenever one deals with an equation of the form ab=c one should be aware of inverse and direct relationships. Here, c represents the revenue which is fixed. Day one mix is 1/2 orangeaide and day 2 mix is 1/3 orangeaide. Since an equal amount of orangeaide is used on both days, the ratio of glasses used from day 1 to day 2 must be 2:3. The price/glass will have an inverse relationship of 2/3. So 2/3rds of .6 =.4 Intern Joined: 26 Sep 2013 Posts: 2 On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 07 Oct 2018, 10:32 OJ: 50L W: 50L TOTAL: 100L 100L*$0.6=$60 OJ: 50 W:100 TOTAL: 150L 150L*X=$60
X=$60/150L=$0.4
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21 Dec 2018, 15:42
This problem is not straightforward because of an implicit assumption that pricing is directly proportional to the amount of orange juice in the drink. Poorly written problems add confusion and waste time. Once you assume what they must be assuming for lack of better guidance it's a relatively easy one.
On a certain day, orangeade was made by mixing a certain &nbs [#permalink] 21 Dec 2018, 15:42
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