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# GMAT Tips: GMAT Mixture Problems

Today’s GMAT tip comes from Kaplan. In this article, Kaplan GMAT instructor Bret Ruber provides tips for answering mixture problems on the GMAT quantitative section:

Two types of mixture problems often appear on the GMAT.  Because these types of problems fall into two very specific categories, we can simply learn the correct strategy for each, and then apply it on test day.

The second type of mixture problem will involve combining two mixtures.  For example, we could be told that mixture X is 10% acid and that mixture Y is 30% acid.  We could then be asked, if, when mixture X and mixture Y are combined, our new mixture is 15% acid, what percent of the new mixture is mixture X?  To solve this problem, set up an equation using the percents you are given.  Let’s use ‘X’ to represent the total amount of mixture X, and  ‘Y’ to represent the total amount of mixture Y. The amount of acid in mixture X is then .1X and the amount of acid in mixture Y is .3Y.  If we add .1X and .3Y, we end up with our total amount of acid, which is 15% of the total mixture.  Therefore, we can say .1X + .3Y = .15(X+Y).  We solve this equation in the following way:

.1X + .3Y = .15(X+Y)

.1X + .3Y = .15X + .15Y

.15Y = .05X

15Y = 5x

3Y = X

X/Y = 3/1

This means that for every 3 parts of mixture X we have 1 part of mixture Y.  The ratio of mixture X to the total is 3 to 4, so mixture X makes up 75% of the total.

Posted in: GMAT - Quantitative, GMAT Tips

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