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by PGMAT » Wed Jun 06, 2012 7:20 pm
Solution X is 25 percent mercury and solution Y is 10 percent mercury. If 12 ounces of solution X are added to 13 ounces of solution Y, approximately what percent of the resulting solution will be mercury?

A)12%
B)17%
C)21%
D)23%
E)37%

What is the easiest way to solve this problem?
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by eagleeye » Wed Jun 06, 2012 7:37 pm
I don't know whether this is the "best" way but it is fast for me. They are asking the average mercury in two solutions:

So : Percent in mixture = (25*12+10*13)/(12+13) = 430/25 = 17.2%.

Let me know if this helps :)
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by Anurag@Gurome » Wed Jun 06, 2012 7:55 pm
PGMAT wrote:Solution X is 25 percent mercury and solution Y is 10 percent mercury. If 12 ounces of solution X are added to 13 ounces of solution Y, approximately what percent of the resulting solution will be mercury?
...

What is the easiest way to solve this problem?
The solution provided by eagleeye is the methodical and traditional one. But particularly for this problem (and many weighted average or allegation problems) an intuitive method is possible which is easier and less time consuming than the traditional one.

If notice carefully, you'll see we are mixing both solution almost by same amount, i.e. 12 and 13 ounces. Hence, the concentration of final solution will be almost midway between the nitital two concentrations.

Hence, final concentration will be approximately equal to (25 + 17)/2 = 34/2 = 17

The correct answer is B.
Anurag Mairal, Ph.D., MBA
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