Mixture problem

[gmat1978]

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 anyone please show me how to solve this problem using alligation approach?

Thanks

[gmatboost]

This question is phrased rather poorly, but I think what it means is:

1 lemon has 0.4 cups of 5% citric acid = 2/5 cups of 1/20 citric acid = 2/100 cups citric acid
She has 4 cups of 12% citric acid = 4 cups of 12/100 citric acid = 48/100 cups citric acid

So she has 24 lemons' worth of citric acid. The recipe calls for 4 lemons, so she can make 6 recipe's worth.

[spoiler]6 * 2 pints water = 12 pints water.[/spoiler]

[hazelnut01]

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.

OA=C

Could someone me with this problem?

[Jay@ManhattanReview]

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.

OA=C

Could someone me with this problem?

We have: 4 lemons need 2 pints of water.

One lemon gives 0.4 cups of 5% citric acid, thus 4 lemons give 0.4*4 = 1.6 cups of 5% citric acid

Marth wants to make lemonade consuming 4 cups of 12% citric acid.

Since 1.6 cups of 5% citric acid need 2 pints of water, 4 cups of 5% citric acid would need 2*(4/1.6) = 5 pints of water

Since 4 cups of 5% citric acid need 5 pints of water, 4 cups of 12% citric acid need 5*(12/5) = 12 pints of water

The correct answer: C

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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[Scott@TargetTestPrep]

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.

The amount of citric acid in the original recipe is 4 x 0.4 x 0.05 = 0.08 cup. The amount of citric acid is 4 x 0.12 = 0.48 cup. We can create the equation where n = the number of pints of water needed for the new recipe:

0.08/2 = 0.48/n

0.08n = 0.96

n = 12

Answer: C