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# GRE Math Challenge #28-Mixture Problems

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GRE Math Challenge #28-Mixture Problems [#permalink]  06 Nov 2015, 19:32
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Expert's post
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Difficulty:

5% (low)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 1 sessions
Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

2.3

A chemist needs to mix a 10 % acid solution with 35% acid solution to end up with 1000 milliters of a 25% acid solution. How much of each solution is needed?
400, 600

If 3 liters of 40% orange juice and 1 liter of 50% orange juice are mixed which of the following is the percentage of orange juice in the mixture?
42.5%

One liquid solution of 7 liters contains 40 % water. A second liquid solution of 18 liters contain 20% water. If these two solutions are mixed, what percent of the mixture is water?
25.6%

Dr. Tik needs to make a solution that is 60% alcohol. if she has 4 liters of a solution that is 25% alcohol, how many of 80% solution will she need to add?
2.5 lit

A mixture of 12 ounces of vinegar and oil is 40%n vinegar by weight. How many ounces of oil must be added to the mixtue to produce a new mixture that is only 25% vinegar?
7.2 ounce

Two solutions of 90% and 97% purity are mixed resulting in 21liters of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?
9 liters

A mixture of 20ltrs of brandy and water contains 10% water. How much water should be added to it to increase the percentage of water to 25%?
4 liters

A cistern contains 50 liters of water. 5 litres of water is taken out of it adn replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.
19/81

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Sandy
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Re: GRE Math Challenge #28-Mixture Problems [#permalink]  05 Jan 2016, 16:16
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hi
could u plz solve it:
Dr. Tik needs to make a solution that is 60% alcohol. if she has 4 liters of a solution that is 25% alcohol, how many of 80% solution will she need to add?
answer: 2.5 or 7 liters of 80%
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Re: GRE Math Challenge #28-Mixture Problems [#permalink]  01 Jul 2017, 11:36
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alime wrote:
hi
could u plz solve it:
Dr. Tik needs to make a solution that is 60% alcohol. if she has 4 liters of a solution that is 25% alcohol, how many of 80% solution will she need to add?
answer: 2.5 or 7 liters of 80%

7 liters is the correct answer.
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Re: GRE Math Challenge #28-Mixture Problems [#permalink]  12 Dec 2017, 11:20
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Expert's post
sandy wrote:

Two solutions of 90% and 97% purity are mixed resulting in 21liters of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?

We can let x = the number of liters of the 90% purity solution and y = the number of liters of the 97% purity solution. We need to determine the value of x.

Since there are 21 liters of the solution:

x + y = 21

y = 21 - x

Since after mixing the two solutions the new mixture has 97% purity:

0.9x + 0.97y = 0.94(x + y)

90x + 97y = 94x + 94y

3y = 4x

Since y = 21 - x, we can substitute 21 - x for y in the equation 3y = 4x:

3(21 - x) = 4x

63 - 3x = 4x

63 = 7x

x = 9
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Jeffrey Miller
Jeffrey Miller

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Re: GRE Math Challenge #28-Mixture Problems [#permalink]  14 Dec 2017, 02:40
sandy wrote:
Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

2.3

A chemist needs to mix a 10 % acid solution with 35% acid solution to end up with 1000 milliters of a 25% acid solution. How much of each solution is needed?
400, 600

If 3 liters of 40% orange juice and 1 liter of 50% orange juice are mixed which of the following is the percentage of orange juice in the mixture?
42.5%

One liquid solution of 7 liters contains 40 % water. A second liquid solution of 18 liters contain 20% water. If these two solutions are mixed, what percent of the mixture is water?
25.6%

Dr. Tik needs to make a solution that is 60% alcohol. if she has 4 liters of a solution that is 25% alcohol, how many of 80% solution will she need to add?
2.5 lit

A mixture of 12 ounces of vinegar and oil is 40%n vinegar by weight. How many ounces of oil must be added to the mixtue to produce a new mixture that is only 25% vinegar?
7.2 ounce

Two solutions of 90% and 97% purity are mixed resulting in 21liters of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?
9 liters

A mixture of 20ltrs of brandy and water contains 10% water. How much water should be added to it to increase the percentage of water to 25%?
4 liters

A cistern contains 50 liters of water. 5 litres of water is taken out of it adn replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.
19/81

=======================================================

I don't understand the logic behind the last questions on proportions of wine and water. Can anyone please explain?

Regards

==========================================================
CEO
Joined: 07 Jun 2014
Posts: 2910
GRE 1: 323 Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 49

Kudos [?]: 836 [1] , given: 146

Re: GRE Math Challenge #28-Mixture Problems [#permalink]  14 Dec 2017, 06:03
1
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Expert's post
Hi,

Initailly we have 50 lts of water in the cistern.

Then we remove 5 liters of water and add 5 liters of wine. So we have 45 lts water and 5 lts wine. Now we remove another 5 lts from the mixture. Now that would remove 0.5 lts of wine and 4.5 lts water.

So New new wine amount is 4.5 + 5 = 9.5 lts of wine and amount of water is 45 - 4.5= 40.5 lts.

Hence ratio is 9.5: 40.5 = 19: 81.
_________________

Sandy
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Re: GRE Math Challenge #28-Mixture Problems   [#permalink] 14 Dec 2017, 06:03
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