Use the 'Translator' to Master Triple Ratios

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This tip for improving your GMAT score was provided by David Newland at Veritas Prep.

Ratio problems are common on the GMAT. But one type of ratio problem seems to present a difficulty for many test-takers: the triple ratio.

A triple ratio is when three items are in ratio to each other, such as flour, water, and sugar, or men, women, and children. To solve a triple ratio, you need to find the “translator.”

The translator is the term that is found in all ratios. For example, if you are told that in a particular animal shelter the ratio of cats to dogs is 7:3 and the ratio of dogs to rabbits is 2:5, you should focus on dogs as the translator.

To use the translator, you need to set the number of dogs equal in both ratios. If the number of dogs is equal, then you will be able to directly compare all three categories. If the number of dogs is not equal, then there is no way to compare the number of cats to the number of rabbits.

Lowest Common Multiple Is the Key
Find the lowest common multiple for the two different numbers of dogs in the two ratios. In one ratio, there are 3 dogs (for every 7 cats). In the other ratio, there are 2 dogs (for every 5 rabbits). The lowest common multiple for dogs is 6 (3 x 2).

Now adjust the number of dogs in each ratio to six and adjust the other animals as well. If the ratio of cats to dogs is 7:3, then with 6 dogs the ratio becomes 14:6. If the number of dogs to rabbits is 2:5, then with 6 dogs the ratio is 6:15.

Since the number of dogs is now the same, the two ratios can be joined using dogs as the translator. The ratio of cats to dogs to rabbits is 14:6:15.

Find the Exchange Rate
Currency exchange rates are one important kind of real-world ratio. Try the following problem from the Veritas Prep Arithmetic book (be sure to use the translator!).

The ratio of the U.S. dollar to the euro is 5:7 and the ratio of the peso to the U.S. dollar is 3:11. What is the ratio of the euro to the peso?

A) 15:77
B) 21:55
C) 55:21
D) 77:15
E) 12:1

This question features a common setup where the question asks for a ratio that does not include the translator. However, to solve the problem you will still need the translator! The only way that you can compare the euro and the peso is if each of them is compared to the same number of dollars.

The numbers of dollars given in the two ratios are 5 (for every 7 euros) and 11 (for every 3 pesos). The lowest common multiple of 5 and 11 is 55. Adjust each ratio for 55 dollars and you get U.S. dollars to euros = 55:77 and pesos to U.S. dollars = 15:55.

The triple ratio then becomes pesos to dollars to euros = 15:55:77. The question asks for the ratio of euros to pesos, and the correct answer is 77:15. Answer choice D is correct.

It may seem like the dollar was not important since it was not part of the answer choices. But the dollar was the most important element of the question. It was the translator. Focus on the translator and master triple ratio questions! (But if you’re traveling internationally this week, use a more current exchange rate; this sample problem is for practice purposes only!)

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