Problem Solving

Hi everyone,

This is question 60 from OG 13 in the problem solving section.

On a certain day, orangeade was made by mixing a certain amount of 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
OA: D

OK, I don't get the logic of this question and the solution that OG and everyone else give. OG and everyone else are like: "OK, so the ratio amount of orangeade made on the first day to amount of orangeade made on the second day is 2:3."

OK, till this part it's correct that the ratio is 2:3, but then they all go on to say: " Thus, the ratio of the number of glasses of orangeade made and sold on the first day to the number of glasses of orangeade made and sold on the second day is 2:3..."

You see, this is the part that I don't get it. You know, I thought about this problem a couple of days and was like : "OK, let me get the logic behind this question. I don't wanna post this easy question on BTG...". My question is that, OK, the ratio of the amount of orangeade made on the first day as opposed to that of the second day is 2:3, but what does this have to do with the number of glasses made and sold on the first and second day?!

Well, if the question was like: " On the second day, orangeade was made by mixing one part orange juice and two parts water...", we were like, OK, orangeade made on the second day is more watery, so customers should be charged less since they're drinking less of orange juice as opposed to yesterday. However, in the question it says: " On the second day, orangeade was made by mixing the same amount of orange juice with twice the amount of water."

Isn't it against your logic? Let's say you make some ice creams one day and sell them for $2 each, the very next day you decide to put a slice of banana beside every ice cream that you sell...wouldn't you charge your customers more than that $2 or at least exactly $2(giving that slice of banana as free)? or would you even lower your price, though you are giving something extra with what you gave yesterday?!!!

I hope my question wouldn't be that dumb, and sorry for this novel that I wrote, I HAD TO give all these explanations to say what is that I don't get it.

Thank you in advance.

javzprobz wrote:Hi everyone,

This is question 60 from OG 13 in the problem solving section.

On a certain day, orangeade was made by mixing a certain amount of 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 each glass = 1 unit.

First day:
Let water = 1 unit and juice = 1 unit.
Glasses = water + juice = 1+1 = 2.
Since each glass earns 60 cents, revenue = 2*60 = 120.

Second day:
Revenue = 120 (same as on the first day).
Since twice as much water is used, water = 2 units.
Juice = 1 unit (same as on the first day.)
Glasses = water + juice = 2+1 = 3.
Price per glass = revenue/glasses = 120/3 = 40.

The correct answer is D.

Mitch, thanks for your solution, but I was trying to understand the logic behind this easy question more. I mean, let's say you decide to check this new cloths store in the town today. You end up buying a pair of jeans for $20. Then, the very next day, you go to this cloths store again and decide to buy another pair of jeans that you bought yesterday. But they tell you that this pair of jeans comes with this pair of socks if you want to buy the jeans. Now, please, tell me, what price do you expect them to charge you today? More than $20 or if you'll be lucky exactly $20 as yesterday ( socks are free with these jeans). But do you expect them to charge you something less than $20?! I hope the part that I don't get is clear now.

By the way, why do you see the problem as 2 glasses and 3 glasses? I see the problem this way : on the first day 1 glass of orangeade consists of 1/2 orange juice and 1/2 water and on the second day 1 glass of orangeade consists of 1/2 orange juice and 2*1/2 water ( 1 water). OK, now I get that it's like on the first day we have 1 glass of orangeade and on the second day we have 3/2 glasses of orangeade. But, again, unfortunately, I don't get those prices. I mean, we are charging 3/2 glasses of orangeade less than 1 glass of orangeade?! Really? OK, maybe I'll be able to solve this question when I'm taking the GMAT, but it doesn't go hand in hand with my logic.

My comments in the attached image.

Here is a video explanation:
https://www.gmatquantum.com/og13/60-prob ... ition.html
Cheers,
Dabral

Thank you so much, Dabral. I just checked your fabulous website...and bookmarked it right away. And thank you for that attached image of your explanation too. OK, one more question, the only reason that we don't consider a price more than 60 cents per glass for the second day is because there is no such choice. We know that the revenues for both days are equal and we don't know if they sold to a less or more or even an equal number of people on the second day. Of course, if they sold to an equal no. of customers, obviously the price would be the same as yesterday (60 cents), but we don't consider this scenario since we don't have such a choice. If we sold to less customers, we would have a higher price per glass, but again since we don't have such a choice so we don't consider it. So we would go with selling each glass cheaper (40 cents) than yesterday.

Am I right? Something tells me my logic isn't that correct too, I don't know.I'm not trying to complicate the problem. Were three scenarios that I mentioned even relevant here? Some clarification is needed, thank you.

javzprobz,

yes, i think you are over analyzing this problem. the key is that the problem says that they sold everything on both days, and their revenue was the same, this is a given condition in the problem. they are selling more of orange juice+water on the second day, and they do end up selling more of the number of glasses, albeit at a lower price.

dabral

Guys.. This is how i understood this problem. Correct me if i am wrong.

First day >> 1 glass of Orange + 1 glass of Water = 2 glasses of Juice. But the shop sells it in a single large glass, which can accommodate 2 glasses of juice, for $0.60 to a customer A
Second day >> 1 glass of Orange + 2 glasses of Water = 3 glasses of Juice. Now the shop uses same large glass to sell the entire juice to customer A. Since the glass can accommodate only 2 glasses of juice, shop has to give the customer A one more half glass of juice (2+1), for the same price $0.60

Hence 1.5 glasses of juice cost $0.60 and the price of 1 glass of juice on second day is 0.60/1.5 = $0.40

Actually, your way of solving this question is quite correct ....and after all, it's such a simple question. I don't know why I was trying to sophisticate the problem and came here and asked those stupid embarrassing questions that have nothing to do with this easy question at all

Hey everybody,

can anyone please explain me what's wrong with my approach:

Let's assume that the cost for each unit of water and orange juice were $0.1. Hence the total cost of one orangeade would be $0.2 on the first day or $0.3 on the second day. The revenue on the first day is: $0.6 - $0.2 = $0.4. Now, since the revenues on both days are equal one can say: $0.4 = price2 - $0.3 => price2 = $0.7.

However this calculation isn't right for any reason?

Best regards!

bs8 wrote: The revenue on the first day is: $0.6 - $0.2 = $0.4.

The revenue in your example is $0.6 per glass...what you charge customers constitutes revenue...revenue net of expenses ($0.6 - $0.2) constitutes earnings.