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m07 #28

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m07 #28  [#permalink]

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New post 05 Nov 2008, 03:23
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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.

Spoiler: :: OA
C

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I cldnt understand the explanation given Can sum 1 explain in more simplified manner?
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New post 05 Nov 2008, 03:51
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amount of citirc acid in 4 lemons = 4*0.4*5/100 (0.4 cups of 5% citric acid from each lemon).

The above amount is required for 2 pints of water.

amount of ctiric acid in 4 cups 12% = 4*12/100

4*0.4*5/100 amount of citric acid requires 2 pints of water.
Hence, 4*12/100 amount of citric acid will require 2*(4*12/100)/(4*0.4*5/100) = 12 pints.
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New post 05 Nov 2008, 04:21
u made the things so simple. Thanks :) U r a genius
scthakur wrote:
amount of citirc acid in 4 lemons = 4*0.4*5/100 (0.4 cups of 5% citric acid from each lemon).

The above amount is required for 2 pints of water.

amount of ctiric acid in 4 cups 12% = 4*12/100

4*0.4*5/100 amount of citric acid requires 2 pints of water.
Hence, 4*12/100 amount of citric acid will require 2*(4*12/100)/(4*0.4*5/100) = 12 pints.
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New post 19 Jul 2010, 00:42
Can you please explain it in detail? esp. the last part.
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Re: m07 #28  [#permalink]

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New post 11 Aug 2010, 09:28
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bibha wrote:
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.
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New post 11 Aug 2010, 23:29
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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)
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New post 12 Aug 2010, 23:51
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Ratio of Citric Acid = 4*0.4*5/100 : 4*12/100 = 1:6
Ratio of Water = 1:6 i.e 2:12
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New post 02 Jun 2011, 10:54
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I'll try to make it simple.

.4 cups from 5% CIRTIC ACID / lemon.

So from 4 lemons we get 1.6 cups of citric acid.

Let 100 ml of citric acid solution exist. So in 1.6 cups we have 1.6*5 = 8 ml of acid/lemonade.

since martha has 4 cups of 12% acid. She has 4*12 = 48 ml of acid. Thus she can make 48/8 = 6 lemonades.

For 1 lemonade we need 2 pints, thus for 6 we need 12 pints.
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Re: m07, #29  [#permalink]

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New post 03 Sep 2011, 23:58
scthakur wrote:
amount of citirc acid in 4 lemons = 4*0.4*5/100 (0.4 cups of 5% citric acid from each lemon).

The above amount is required for 2 pints of water.

amount of ctiric acid in 4 cups 12% = 4*12/100

4*0.4*5/100 amount of citric acid requires 2 pints of water.
Hence, 4*12/100 amount of citric acid will require 2*(4*12/100)/(4*0.4*5/100) = 12 pints.


The answer is C. The trick is to identify that you need to know the precise amount of Citric acid.
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New post 20 Apr 2012, 12:45
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ritula wrote:
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.

Spoiler: :: OA
C

Source: GMAT Club Tests - hardest GMAT questions

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.

Answer: C.
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New post 16 Aug 2012, 05:30
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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.

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Re: m07 #28  [#permalink]

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New post Updated on: 17 Aug 2012, 19:45
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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?

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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Originally posted by hafizkarim on 16 Aug 2012, 05:44.
Last edited by hafizkarim on 17 Aug 2012, 19:45, edited 1 time in total.
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New post 16 Aug 2012, 06:21
what percentile question is it. it seemed very tough
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New post 16 Aug 2012, 06:33
Acid in recipe (with 4 lemons): 4*0.4*5/100=.08 or 8/100
Marta has: 4*12/100=48/100

48/100 is 6 times 8/100. So Marta will need 6(2 pints) of water--> 12 pints--> C
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New post 16 Aug 2012, 08:33
mailpravs wrote:
Ratio of Citric Acid = 4*0.4*5/100 : 4*12/100 = 1:6
Ratio of Water = 1:6 i.e 2:12

that was very quick. thanks
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New post 27 Mar 2014, 04:30
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ritula wrote:
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

4 lemons contains.
Acid = 0.08
Residual (water) = 1.52

4 cups of Citric acid concentrate contains 12% Citric acid and 88% Residual (water)
Thus \(Acid = \frac{12}{100} * 4 --- and --- residue-liquid (water) = \frac{88}{100} * 4\)
Acid = 0.48 cups
residue liquid (water) = 3.52 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.

\(Water- required -as- per- the- ratio- provided = 2 * 6 + 5.6 missing- residue- liquid-(water) = 12 + 5.6 = 17.6 (cups- of- water)\)

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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Re: m07 #28   [#permalink] 27 Mar 2014, 04:30
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