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To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. One can squeeze out 0.4 cups of 5% citric acid from an average lemon. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. She has sugar and water in abundance. How much water will Marta use?
(A) 2 pt. (B) 6 pt. (C) 12 pt. (D) 15 pt. (E) 100 pt.
Can you please explain it in detail? esp. the last part.
To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. One can squeeze out 0.4 cups of 5% citric acid from an average lemon. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. She has sugar and water in abundance. How much water will Marta use?
standard recipe: 4 lemons; 30 ounces of water; 2 pts of water
we want to know amount of water required to use- with 4 cups of 12% citric acid i.e 48/100 acid
1 lemon contains 0.4 cups of 5% acid 4 lemons contain 4 x 0.4 x 5% = 8/100 acid
48/100 = 6 x (8/100) --> amount of water (proportionally) = 6 x 2 = 12 pts hope my explanation helps. _________________
KUDOS me if you feel my contribution has helped you.
In the orginal receipt you see, that you need 0,08 cups of citric acid. Why? -> 4 lemons contains 1,6 cups 5% citric acid. Therefore 1,6 * 5 /100 = 0,08 cups of 100% citric acid
In the question you have 4 cups of 12% citric acid, meaning you have 0,48 cups of 100% citric acid (= 4 * 12 / 100)
In the first receipt you have 2 pt of water for 0,08 cups citric acid, that means that you need 12 pt of water for 0,48 cups of citric acid (= 2 / 0,08 * 0,48)
To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. One can squeeze out 0.4 cups of 5% citric acid from an average lemon. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. She has sugar and water in abundance. How much water will Marta use?
(A) 2 pt. (B) 6 pt. (C) 12 pt. (D) 15 pt. (E) 100 pt.
I cldnt understand the explanation given Can sum 1 explain in more simplified manner?
Standard recipe requires: 4 lemons and 2 pints of water. 4 lemons contain \(4*0.4*\frac{5}{100}=\frac{8}{100}\) cups of citric acid;
Now, Marta has \(4*\frac{12}{100}=\frac{48}{100}\) cups of citric acid, so 6 times as many as the standard recipe requires (48/8=6), which means that she'll need 6 times as many water as the standard recipe requires. Hence she'll need 6*2=12 pints of water.
When GMAT life gives you lemonade, think lemons...
The initial data is in terms of lemons, specifically 4 lemons to make a given lemonade recipe. We need how many lemons are used to make given quantity of citric acid. And we are told that 1 lemon contains 0.4 cups of 5% citric acid===> 0.4 cups * 5% per lemon= 2% cups (of citric acid) per lemon And we are given 4 cups of 12% citric acid= 48% cups of citric acid, which corresponds to 48%/2% lemons= 24 lemons
Since we know that 24 lemons were used to make our citric acid, the constant of proportion is 24 lemons/4 lemons = 6. Therefore we need 2 pints*6= 12 pints of water.
To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. One can squeeze out 0.4 cups of 5% citric acid from an average lemon. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. She has sugar and water in abundance. How much water will Marta use?
Lets Break this down a bit. First of all, what the heck does 5% Citric Acid mean ? ! Well, in 100 ml of water, you have 5 ml of Citric Acid. So far , so good.
Also, when talking in terms of cups, 5% Citric Acid means that you have 5/100 Cups of Citric Acid. The exact size of the cup doesn't matter. The cup can be a small cup, big cup, medium sized cup, it doesn't matter. Here we are talking in terms of percentages.
The key to this question is convert the percentage of citric acid into more absolute terms, so that we can start comparing apples to apples.
From one lemon, you can squeeze out 0.4 Cups of 5 % citric Acid. What does thie mean ? You can squeeze out 0.4 x 5 /100 cups of citric Acid ==> 2/100 cups of Citric Acid The recipe requires 4 Lemons and 2 Pints of Water This implies 4 x 2/100 cups of Citric Acid are to mixed with every 2 Pints of Water
8/100 cups of Citric Acid : 2 Pints of Water ...Lets call this (1)
Martha has 4 Cups of 12 % Citric Acid. Which means that she has 4 x 12/100 cups of Citric Acid = 48 /100 cups of Citric Acid
The amount of water she has to add must be in the same proportion as (1) Hence 8/100 : 2 = 4 x 12/100 : x x = 12
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Last edited by hafizkarim on 17 Aug 2012, 18:45, edited 1 time in total.
To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. One can squeeze out 0.4 cups of 5% citric acid from an average lemon. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. She has sugar and water in abundance. How much water will Marta use?
(A) 2 pt. (B) 6 pt. (C) 12 pt. (D) 15 pt. (E) 100 pt.
I think Answer should be 17.6 cups : Here is my solution :
One lemon contains 0.4 cups juice concentration 5% acid and 95% of residue liquid (water). Thus \(Acid = \frac{5}{100} * 0.4 --- and --- residue-liquid (water) = \frac{95}{100} * 0.4\) Acid = 0.02 cups Residual (water) = 0.38 cups
To calculate number of lemons which contain equivalent citric acid. \(No- of- Lemons = \frac{0.48}{0.02} = 24\) \(residue-liquid-(water)- in- 24- lemons = 0.38 * 24 = 9.12\)
residue liquid (water) available from 4 cups of Citric acid is 3.52 cups , but 24 lemons provide 0.38 * 24 = 9.12 cups. Thus in Lemonade we will have to add 9.12-3.52 cups to balance the missing residue liquid (water) \(9.12 - 3.52 = 5.6 cups\)
Using 4 cups of 12% Citric acid we can make 24/4 = 6 servings of lemonade.
If we do not add this 5.6 cups of liquid water Martha will get highly concentrated Citric lemonade. Further as ratios are not given in Citric : sugar : water instead given as lemon : sugar : water we must consider to add missing residue else in final mixture fraction of Citric will be higher compared to other ingredient and final ratio wont be same as provide in recipe. _________________
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