Carcass wrote:
If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?
A. 3%
B. 20%
C. 66%
D. 75%
E. 80%
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math BookWhen solving mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED.
Since we're asked to find a PERCENTAGE, we can assign a "nice" value to the original volume.
So, let's say we start with 100 liters
As you can see, 50 liters is alcohol and 50 liters is water
Now let's remove
x liters of the mixture from the container.
Half of removed x liters will be alcohol, half of the removed x liters will be water
In other words, we're removing 0.5x liters of alcohol, and 0.5x liters of water.
So, the resulting mixture looks like this:
We're going to replace the x liters of missing solution with x liters of 25% alcohol solution
When we add the volumes of alcohol and water, we get a final mixture that looks like this:
Finally, we want the final mixture to be 30% alcohol.
In other words, we want: (volume of alcohol)/(total volume of mixture) = 30/100 (aka 30%)
We get: (50-0.25x)/100 = 30/100
Cross multiple: (50-0.25x)(100) = (100)(30)
Simplify: 5000 - 25x = 3000
Solve to get: x = 80
So, 80 liters were originally removed
Answer: E