Mixture problem

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gmat1978: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Thu Dec 23, 2010 7:38 pm

Mixture problem

by gmat1978 » Sat Aug 13, 2011 9:10 pm

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

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Source: Beat The GMAT — Problem Solving | Sat Aug 13, 2011 9:10 pm

gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pm; Location: New York City; Thanked: 130 times; Followed by:33 members; GMAT Score:780

by gmatboost » Mon Aug 15, 2011 9:34 am

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]

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hazelnut01: Master | Next Rank: 500 Posts; Posts: 157; Joined: Sat Nov 19, 2016 5:34 am; Thanked: 2 times; Followed by:4 members

by hazelnut01 » Wed May 17, 2017 9:21 pm

gmat1978 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.

OA=C

Could someone me with this problem?

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GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Thu May 18, 2017 9:23 am

ziyuenlau wrote:
gmat1978 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.

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: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Mixture problem

by Scott@TargetTestPrep » Sat Apr 11, 2020 8:07 am

gmat1978 wrote: ↑
Sat Aug 13, 2011 9:10 pm
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

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