Quantitative Reasoning: Making Ratios Rational

The GRE quantitative reasoning section contains many different types of questions, some of which can be on the difficult side, but the GRE prep experts at Testmasters are here to help you through the ins and outs of solving even the hardest of math problems on this exam.

Today, we look at ratios. Though there are many forms, most ratios are given in either fraction form or with a colon, but both forms are comparing parts to parts. The secret to most ratio problems is to first identify the total number of parts that you’re dealing with. Once that is known, you can take those parts and use the total to find fractional amounts or to solve for probability.

Here is an example of how the total in a ratio problem can help you to find a fractional amount:

A cocktail contains various ingredients: club soda, hard apple cider, brandy, and vodka. A bartender uses a ratio of 9:5:4:2 respectively to mix the ingredients by volume. How much vodka should the bartender use to prepare a 6-oz drink?

Solve this problem by first finding the total number of parts. Simply add the ratio amounts together to get the total:


Recall that a fraction is equal to the part over the total. The part of the mixture that is vodka is 2, and the total number of parts are 20; therefore, the fraction of the drink that is vodka is equals 1 over 10.

Multiply this fraction by the total number of ounces in the final drink to determine the amount the bartender should pour into a 6-oz drink.

equals 0.6

There will only be 0.6 oz. of vodka in a 6-oz. drink, and using this same method, you could solve for the amounts of the other ingredients, too. Try it yourself. How many ounces of club soda, hard apple cider, and brandy would each be in the 6-oz. drink? The answers are below. No peeking until after you’re done.


Club soda:  2.7 ounces club soda 2.7

Hard apple cider: 1.5 ounces hard apple cider 1.5

Brandy: 1.2 ounces brandy 1.2

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