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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # On a certain day, orangeade was made by mixing a certain  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Senior Manager Affiliations: UWC Joined: 09 May 2012 Posts: 364 Location: Canada GMAT 1: 620 Q42 V33 GMAT 2: 680 Q44 V38 GPA: 3.43 WE: Engineering (Entertainment and Sports) On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 24 May 2012, 22:32 6 38 00:00 Difficulty: 45% (medium) Question Stats: 66% (02:00) correct 34% (02:22) wrong based on 829 sessions ### HideShow timer Statistics 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. $0.15 B.$0.20
C. $0.30 D.$0.40
E. $0.45 ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 25 May 2012, 00:49 18 13 macjas 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. $0.15 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=$0.4. Answer: D. Hope it's clear. _________________ ##### Most Helpful Community Reply Intern Joined: 21 Oct 2011 Posts: 9 Schools: Insead '13 Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 03 Jun 2012, 05:20 5 1 Bunuel Is it ok to plugin for this sum. 100 ltrs of the orangeade= 50 W + 50 Concentrate 150 ltrs of the orangeade-= 100W + 50 concentrate since total revenue is the same 100*.6 = 150* x thus x = 0.4 Can i take the above approach? ##### General Discussion Intern Status: ISB 14...:) Joined: 25 May 2012 Posts: 29 Location: India Concentration: Strategy Schools: ISB '14 (A) GMAT 1: 750 Q51 V39 GPA: 3.62 WE: Engineering (Energy and Utilities) Re: maths problems [#permalink] ### Show Tags 06 Jun 2012, 23:32 Let the amount of orange juice be X. Orangeade made on first day = X + X(same amount of water) = 2X Orangeade made on second day = X + 2X (twice the amount of water) = 3X So the total number of glasses made will be of the ratio 2:3 As total revenue is same on both days, (2)(0.16) = (3)(Price on second day) Price per glass on second day = 0.32/3 = 0.107 SVP Joined: 06 Sep 2013 Posts: 1720 Concentration: Finance Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 05 Feb 2014, 12:07 2 1 I really like this one So first you sold 1:1 water and orange, let's say a liter of each so total per glass is 2 liters After you sold 2:1 water and orange, let's say a liter of each again so total per glass is 3 liters Now since the revenue is the same and the ratio in the quantity increased to 3/2 then the price has to be the inverse 2/3 So 0.6 * 2.3 - 0.4 Answer is D Hope it clarifies Cheers J Manager Joined: 25 Mar 2013 Posts: 240 Location: United States Concentration: Entrepreneurship, Marketing GPA: 3.5 Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 23 Aug 2014, 01:20 On fist day 0.60$ per glass and assume sold 10 glasses of orange = 6$On next Day on adding double amount of water, might sold 20 glasses of orange , so 0.30$ x 20 = 6 $So C But My answer is wrong... Even i understood Above solutions, But why analysis is wrong Pls help _________________ I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 23 Aug 2014, 11:31 kanusha 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. $0.15 B.$0.20
C. $0.30 D.$0.40
E. $0.45 On fist day 0.60$ per glass and assume sold 10 glasses of orange = 6$On next Day on adding double amount of water, might sold 20 glasses of orange , so 0.30$ x 20 = 6 $So C But My answer is wrong... Even i understood Above solutions, But why analysis is wrong Pls help On the first day orangeade was made by mixing a certain amount of orange juice with an equal amount of water. So, if 10 glasses of orangeade was sold on the first day, then it was made by mixing 5 glasses of orange juice with 5 glasses of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water, so it was made with 5 glasses of orange juice and 10 glasses of water, which makes total of 15 glasses of orangeade. 10*0.6 = 15*x --> x = 0.4. Hope it's clear. _________________ Manager Joined: 02 Sep 2014 Posts: 71 Location: United States Concentration: Strategy, International Business GMAT 1: 700 Q49 V37 GMAT 2: 700 Q47 V40 GMAT 3: 720 Q48 V41 GPA: 3.26 WE: Consulting (Consulting) On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 13 Dec 2014, 15:11 I also like this question. I just wanted to post another way to think about this question. The first day was a ratio of 1:1, which gives a total of 2 parts: 1L + 1W = 2X The second day was a ratio of 1:2, which gives a total of 3 parts: 1L + 2W = 3X Since the revenue was the same for both says, and since there was a quantity increase of 50% (3 is an increase of 50% from 2), you can think of the answer this way: What number when increased by 50% equals .6? That number is .4 Also, as previously mentioned, since the increase was 3/2, you can also multiply .6 by 2/3, which is the inverse of 3/2. Admittedly, this method is probably better. I just wanted to point out a different method / different way to think about the problem. Manager Joined: 10 Jun 2015 Posts: 118 Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 14 Aug 2015, 05:15 1 macjas 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. $0.15 B.$0.20
C. $0.30 D.$0.40
E. $0.45 1o +1w = 2j*0.60=1.20 1o + 2w= 3j*0.40=1.20 the correct option is D Intern Joined: 04 Feb 2014 Posts: 13 Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 11 Sep 2015, 06:32 when people are saying of multiplying by the inverse, do we do this because the price was the same? Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4295 Location: United States (CA) Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 02 May 2016, 07:27 macjas 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. $0.15 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 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 don’t know the price per glass on day 2, so let’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. Answer D. _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Director Status: Professional GMAT Tutor Affiliations: AB, cum laude, Harvard University (Class of '02) Joined: 10 Jul 2015 Posts: 671 Location: United States (CA) Age: 39 GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42 GRE 1: Q168 V169 WE: Education (Education) On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags Updated on: 07 Dec 2016, 19:08 Attached is a visual that should help. Part of the key here is realizing that a "glass" is a constant, and that you can insert numbers to "make it true". Attachments Screen Shot 2016-12-07 at 7.06.07 PM.png [ 144.29 KiB | Viewed 7979 times ] _________________ Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002. One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong). You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979. GMAT Action Plan and Free E-Book - McElroy Tutoring Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club.) ...or find me on Reddit: http://www.reddit.com/r/GMATpreparation Originally posted by mcelroytutoring on 17 May 2016, 18:25. Last edited by mcelroytutoring on 07 Dec 2016, 19:08, edited 5 times in total. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8678 Location: Pune, India Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 18 May 2016, 01:23 1 macjas 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. $0.15 B.$0.20
C. $0.30 D.$0.40
E. $0.45 Revenue = Number of glasses * Price per glass On second day, twice the amount of water was added so number of glasses was 3/2 the number of glasses on first day. Revenue on both days was the same so N * 0.6 = (3N/2) * Cost on day 2 Cost on day 2 = 0.4 Answer (D) _________________ 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 > VP Joined: 07 Dec 2014 Posts: 1128 Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 09 Jun 2017, 19:01 macjas 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. $0.15 B.$0.20
C. $0.30 D.$0.40
E. $0.45 g=number of glasses sold day 1 x=price per glass day 2 r=revenue both days g*.6=r 3/2*g*x=r 3/2*g*x=g*.6 x=$.40
D
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On a certain day, orangeade was made by mixing a certain  [#permalink]

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08 Apr 2018, 04:50
macjas 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.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45

why is my reasoning wrong UPDATE I noticed one mistake, so I corrected it but still dont get how to reach final solution

first day: 1 litre of juice +1 litre of water hence ratio---> 1:1 (total 2 litres)

Second day: 1 litres of juice +2 litres of water hence ratio---> 1:2 ( total 3 litres )

If ratio of mixture on day one to mixture on day two is 2 to 3 and price per glace on day one is 0.60

so i assume from this ratio $$2:3$$ that $$2$$ is 0.60 and what to do next if $$2$$ is 0.60 then what is $$3$$ how to calculate

or where am i wrong
VP
Joined: 09 Mar 2016
Posts: 1230
Re: On a certain day, orangeade was made by mixing a certain  [#permalink]

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08 Apr 2018, 05:11
Bunuel wrote:
macjas 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.$0.15
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.

Answer: D.

Hope it's clear.

Bunuel can you explain the logic when we receive the ratio, know the price of glass 0.60

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

I dont get why are you multiplying 0.60 by 2 ( 0.60 costs one glass and not two litres ) right ? if 2 were number of glasses than it would be ok....
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Re: On a certain day, orangeade was made by mixing a certain  [#permalink]

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09 Apr 2018, 00:15
1
dave13 wrote:
macjas 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.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45

why is my reasoning wrong UPDATE I noticed one mistake, so I corrected it but still dont get how to reach final solution

first day: 1 litre of juice +1 litre of water hence ratio---> 1:1 (total 2 litres)

Second day: 1 litres of juice +2 litres of water hence ratio---> 1:2 ( total 3 litres )

If ratio of mixture on day one to mixture on day two is 2 to 3 and price per glace on day one is 0.60

so i assume from this ratio $$2:3$$ that $$2$$ is 0.60 and what to do next if $$2$$ is 0.60 then what is $$3$$ how to calculate

or where am i wrong

Note that Revenue is the same on both the days. That is the information that will give you the relation between 2:3 and 0.60.

Revenue = Unit Price * Volume sold

UnitPrice1 * VolumeSold1 = UnitPrice2 * VolumeSold2

VolumeSold1 / VolumeSold2 = UnitPrice2 / UnitPrice1

2/3 = UnitPrice2 / 0.60

UnitPrice2 = 0.40
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On a certain day, orangeade was made by mixing a certain  [#permalink]

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29 Apr 2018, 18:27
1
macjas 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.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45

LET THE TOTAL QUANTITY OF THE MIXTURE BE 'X'
FIRST DAY: AMOUNT OF ORANGEADE = 1/2X
SECOND DAY: AMOUNT OF ORANGEADE = 1/3X [ SINCE 2 PARTS ARE WATER AND ONE PART IS ORANGEADE ]

SINCE THE AMOUNT QUANTIFIES ONLY TO THE ORANGEADE WHILE WATER IS CONSIDERED TO HAVE NO COST -

FIRST DAY : (1/2) X = 0.60
THEREFORE, SECOND DAY : (1/3) X = (0.60 * 2)/3 = 0.40 [ CHOICE D ]
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Re: On a certain day, orangeade was made by mixing a certain  [#permalink]

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14 Aug 2018, 02:17
Let the quantity in volume be "x".
First case revenue=2x*0.60 (orange:water=1:1 and price per cup is 0.60)
Second case revenue=3x*P (orange:water=1:2 and price per cup is "P")
As they have mentioned revenue is same,
2x*0.60=3x*P
P=0.40

Answer (D)
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Re: On a certain day, orangeade was made by mixing a certain  [#permalink]

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14 Aug 2018, 05:03
macjas 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.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45

Plug in values in terms of GLASSES.

On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water.
The orangeade was sold at \$0.60 per glass on the first day.

Let the total orangeade = (1 glass juice) + (1 glass water) = 2 glasses.
Since each glass sells for 60 cents, the revenue = 2*60 = 120 cents.

On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water.
Orangeade = (1 glass juice) + (2 glasses water) = 3 glasses.

The revenue from selling the orangeade was the same for both days.
What was the price per glass on the second day?

Since the revenue for the 3 glasses on the second day remains 120 cents, the price per glass $$= \frac{120}{30} = 40$$ cents.

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