yellowho wrote:A chemist combined a milliliters of a solution that contained 20
percent substance S, by volume, with b milliliters of a solution
that contained 8 percent substance S, by volume, to product c
milliliters of a solution that was 10 percent substance S, by
volume. What is the value of a?
(1) b = 20
(2) c = 24
How is D(OA) possible?
The following method is called
alligation. It's an easy way to handle weighted average problems.
To combine a 20% solution with an 8% solution to yield a 10% solution:
The proportion needed of each starting percentage is the positive difference between the other 2 percentages.
Proportion needed of a (20% solution) = 10-8 = 2.
Proportion needed of b (8% solution) = 20-10 = 10.
Thus, a:b = 2:10 = 1:5.
We also know that a+b = c.
Statement 1: b = 20
Since a:b = 1:5 and b = 20, we know that a = 4, yielding a ratio of 4:20 = 1:5.
Sufficient.
Statement 2: c = 24
a+b = 24.
Since a:b = 1:5, a = 4 and b = 20.
Sufficient.
The correct answer is
D.
An important take-away:
Since all the percentages are given -- the two original percentages as well as the percentage in the final mixture -- knowing any one of the values (a, b, or c) will allow us to determine the other 2 values. Thus, without doing any math, we can quickly see that each statement is sufficient.
Last edited by
GMATGuruNY on Fri Feb 18, 2011 8:08 am, edited 1 time in total.
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