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Solution Y is 40 percent sugar by volume, and solution X is 20 percent
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19 May 2021, 05:07
19 May 2021, 05:07
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Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. How many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume?
(A) 37.5
(B) 75
(C) 150
(D) 240
(E) 450
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) 37.5
(B) 75
(C) 150
(D) 240
(E) 450
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Joined: 10 Apr 2015
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Re: Solution Y is 40 percent sugar by volume, and solution X is 20 percent
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19 May 2021, 06:10
19 May 2021, 06:10
Carcass wrote:
Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. How many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume?
(A) 37.5
(B) 75
(C) 150
(D) 240
(E) 450
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) 37.5
(B) 75
(C) 150
(D) 240
(E) 450
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
When solving mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED.
Start with 150 gallons of solution that is 40% sugar:
When we draw this with the ingredients separated, we see we have 60 gallons of sugar in the mixture.
Next, we'll let x = the number of gallons of solution X we need to add.
Since 20% of the solution X is sugar, we know that 0.2x = the volume of sugar in this solution:
At this point, we can ADD the two solutions (PART BY PART) to get the following volumes:
Since the resulting solution is 25% sugar (i.e., 25/100 of the solution is sugar), we can write the following equation:
(60 + 0.2x)/(150 + x) = 25/100
Simplify to get: (60 + 0.2x)/(150 + x) = 1/4
Cross multiply to get: 4(60 + 0.2x) = 1(150 + x)
Expand: 240 + 0.8x = 150 + x
Rearrange: 90 = 0.2x
Solve: x = 450
Answer: E
Re: Solution Y is 40 percent sugar by volume, and solution X is 20 percent
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28 Dec 2023, 16:01
28 Dec 2023, 16:01
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