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: |
|
| GMAT Club Forum https://gmatclub.com:443/forum/ |
|
| On a certain day, orangeade was made by mixing a certain https://gmatclub.com/forum/on-a-certain-day-orangeade-was-made-by-mixing-a-certain-133206.html |
Page 1 of 2 |
| Author: | macjas [ May 24, 2012 ] |
| Post subject: | On a certain day, orangeade was made by mixing a certain |
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 |
|
| Author: | Bunuel [ May 25, 2012 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
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=$0.4. Answer: D. Hope it's clear. |
|
| Author: | yogeshwar007 [ Jun 3, 2012 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
Bunuel Is it ok to plugin for this sum. 100 ltrs of the orangeade= 50 W + 50 Concentrate 150 ltrs of the orangeade-= 100W + 50 concentrate since total revenue is the same 100*.6 = 150* x thus x = 0.4 Can i take the above approach? |
|
| Author: | gnan [ Jun 7, 2012 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
Let the amount of orange juice be X. Orangeade made on first day = X + X(same amount of water) = 2X Orangeade made on second day = X + 2X (twice the amount of water) = 3X So the total number of glasses made will be of the ratio 2:3 As total revenue is same on both days, (2)(0.16) = (3)(Price on second day) Price per glass on second day = 0.32/3 = 0.107 |
|
| Author: | jlgdr [ Feb 5, 2014 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
I really like this one So first you sold 1:1 water and orange, let's say a liter of each so total per glass is 2 liters After you sold 2:1 water and orange, let's say a liter of each again so total per glass is 3 liters Now since the revenue is the same and the ratio in the quantity increased to 3/2 then the price has to be the inverse 2/3 So 0.6 * 2.3 - 0.4 Answer is D Hope it clarifies Cheers J |
|
| Author: | kanusha [ Aug 23, 2014 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
On fist day 0.60$ 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 |
|
| Author: | Bunuel [ Aug 23, 2014 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
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. |
|
| Author: | pate13 [ Dec 13, 2014 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
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. |
|
| Author: | mathivanan [ Aug 14, 2015 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
1o +1w = 2j*0.60=1.20 1o + 2w= 3j*0.40=1.20 the correct option is D |
|
| Author: | ScottTargetTestPrep [ May 2, 2016 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
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. |
|
| Author: | mcelroytutoring [ May 17, 2016 ] | ||
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain | ||
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".
|
|||
| Author: | KarishmaB [ May 18, 2016 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
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) |
|
| Author: | dave13 [ Apr 8, 2018 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
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  if how to calculate or where am i wrong
|
|
| Author: | KarishmaB [ Apr 9, 2018 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
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 |
|
| Author: | jalice [ Aug 14, 2018 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
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) |
|
| Author: | GMATGuruNY [ Aug 14, 2018 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
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 |
|
| Author: | avigutman [ Jul 16, 2021 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
Video solution from Quant Reasoning starts at 0:27 Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 |
|
| Author: | naveeng15 [ Jan 7, 2022 ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
o 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 |
|
| Author: | Dereno [ Feb 24 at 03:12am ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
Let us consider a glass of water = glass of orange juice = x Initial , one glass of water mixed with one glass of orange juice = x+x = 2x Price per glass is $0.6 Revenue = 0.6*2x = 1.2x Now, one glass orange juice mixed with two glasses of water = x+ 2x = 3x this 3x generates the same revenue of 1.2x 3x * (Rate per glass) = 1.2x Rate per glass = $ 0.4 |
|
| Author: | NoraUnoSama [ Feb 25 at 01:25pm ] |
| Post subject: | Re: On a certain day, orangeade was made by mixing a certain |
On the first day 0.5 Vol of Orange + 0.5 Vol of Water gave 1 Volume of Orangeade On the second day 0.5 Vol of Orange + 1 Vol of Water (twice the vol of Orange ) gave 1.5 Vol of Orangeade Sold at the Same revenue, we have 1* 0.6 = 1.5 x where 0.6 is the price on the first day and x that on the second. x = 0;6*(1/1.5) = 0.6*(1/1)*(2/3) = 1.2 / 3 = 0.4$ = Answer D. |
|
| Page 1 of 2 | All times are UTC - 8 hours [ DST ] |
| Powered by phpBB © phpBB Group http://www.phpbb.com/ |
|