Land Your Score: Ratio Problems

Welcome to “Land Your Score,” a blog series in which Kaplan instructor Jennifer Land shares key insights and strategies for improving your GMAT performance on Test Day. This week, Jennifer discusses how to approach Quantitative Reasoning ratios using the Kaplan Method.

Ratio problems on the GMAT

Ratio problems often give test-takers fits. Most of us remember how to work with ratios, but when faced with a ratio in a GMAT Quantitative Reasoning problem, that memory tends to fade.

The key to solving ratio problems is mastering the basic principles involved, which is what this post will help you do.

Ratio = The relationship between quantities

A ratio shows you the proportional relationship between two or more quantities of items. It does not tell you how many of each item you have; instead, it is the reduced fraction of the proportional relationship. For example, in a classroom with 8 girls and 6 boys, the two quantities are 8 and 6. This becomes the fraction 8/6, which we can reduce to 4/3.

Ratios can be represented as actual fractions or with a colon between the quantities, or even with the word “to” between the numbers. In our classroom example, we can say the ratio is 4 to 3, 4:3, or 4/3. When you have more than two quantities, you will probably want to use the colon notation.

Relationships between more than two quantities

Here is a sample Quantitative Reasoning problem with three quantities, a three-part ratio:

If the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 5, what is the ratio of apples to cucumbers?

 

4:15

1:3

2:5

4:5

7:6

 

We will use the Kaplan Method for Problem Solving to tackle this one.

 

Step 1. Analyze the question. What do you know? You know the relationships between two pairs of quantities, apples and bananas, and bananas and cucumbers.

 

Step 2. State the task. What do you need to know? You need the relationship between apples and cucumbers.

 

Step 3. Approach strategically. For most ratio problems, the best approach is the straightforward math. The problem gives you the information you need; you just need to determine how to use it.

 

Here is the key: Whenever you have a three-part ratio, make the shared quantity the same. In this ratio problem, that is the quantity of bananas. The problem tells us the ratio of apples to bananas is 4 to 3. Then it tells us the ratio of bananas to cucumbers is 1 to 5—wait! We know from the first ratio that we have to have at least 3 bananas. If there were only 1 banana, the first ratio wouldn’t make sense. (There are no partial fruits, vegetables, or any other quantity on the GMAT.)

 

In order to make the two ratios work together, we have to have 3 bananas. Now think about the second ratio; if you have 3 bananas, the way to “convert” the number of bananas in the second ratio to 3 is to multiply the entire ratio by 3. So a ratio of 1:5, when multiplied by 3, becomes 3:15.

 

Now you can line the ratios up, because their common currency, bananas, is now the same. The two ratios are now speaking the same language. We now know that apples to bananas to cucumbers is 4 to 3 to 15. Because the problem isn’t asking us about bananas—we just used them to find the answer—we can throw them out. In the end, the ratio of apples:cucumbers = 4:15.

 

Step 4. Confirm your answer. Does this answer make sense? Yes, it does. Ratio problem solved!

 

Want to master ratio problems? Visit Kaptest.com/gmat to explore our course options.

 

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