Strategies, Sample Questions, and Random Ramblings.
July 19, 2015
GMAT mixtures come in a variety of different forms, but generally mixture problems are just weighted average problems. There are a few differences that we will go over, but think of them in the same manner. This is an example:
Solution A consists of 20% iodine and solution B is 5% iodine. If 15 ounces of solution B is mixed with solution A to make a combined solution of 10%, how many ounces of solution A are used?
For this we can just set up a weighted average problem:
We will use the same technique (subtracting the smallest value) in order to simplify the math. After subtracting 5, we get the following:
Then, solve for x:
We are done now and do not need to add the 5 back because that was related to the value not the weight. With a little practice this will be easy.
Another way that you can solve this can save you a bit of time is to use the transposition method; in fact, this can be used on other types of weighted average problems as well.
This may take a bit of time to understand, but can be a true time saver on the exam. The key piece of information: The ratio of the weighting of two mixtures is equal to the inverse of the positive difference of the values themselves and the weighted average. Let’s do this with the previous example.
This means that the ratio of the 5% solution to the 20% solution is 10:5 or 2:1. Thus, if there were 15 ounces of the 5% solution, there would be half (or 7.5 ounces) as many ounces of the 20% solution.
This can be applied to a lot of different problems so look at the answer explanations to the questions to make sure you get this right. This method is particularly helpful if you are given the two mixtures and the combined mixture. Often times you will be asked to find the ratio of the solutions and this simple subtraction will help you find it.
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