Ratios are a common topic for the word problems that you can expect to see on the GRE. This article will discuss some of the basic properties of ratios and help you recognize and solve both part-to-part and part-to-whole ratio questions. To start, let’s discuss what a ratio is.


In its simplest form, a ratio compares two quantities. For example, if there are 5 cats and 6 dogs in a room, we can say that the ratio of the number of cats to the number of dogs is 5 to 6. Equivalently, we can say that for every 5 cats in the room, there are 6 dogs.

Now suppose instead that the room contains 10 cats and 12 dogs. By dividing the cats and dogs each into two equal groups, we can still say that for every 5 cats in the room, there are 6 dogs. So, the ratio of the number of cats to the number of dogs is still 5 to 6.

We can express ratios in three equivalent ways. Using the previous example, we can express the ratio of cats to dogs as any of the following:

1. cats to dogs = 5 to 6
2. cats : dogs = 5 : 6
3. cats/dogs = 5/6

While the GRE might use any of these three notations, we will use the fractional ratio when solving ratio questions in the problems that follow.


To successfully solve ratio questions on the GRE, we need to understand the information a ratio provides. A ratio allows us to determine both of the following relationships:

1. How one part of a ratio relates to the other part
2. How one part of a ratio relates to the whole or total

Going back to the cat and dog example, we express the part-to-part ratio of cats to dogs as 5 to 6, or 5/6, because there are 5 cats for every 6 dogs in the room.

We can also use this information to determine a part-to-whole ratio. Because we have 5 cats and 6 dogs, we know that the total number of animals in the room is 6 + 5 = 11. So, the part-to-whole ratio of cats to total is 5 to 11, or 5/11, and the part-to-whole ratio of dogs to total is 6 to 11, or 6/11.

The major takeaway is that if we have a ratio that compares a part to a part, we can use that information to determine the ratio that compares a part to a whole.

Let’s practice with another example:

If the ratio of girls to boys in a class is 4 to 3, and all students in the class are either boys or girls, then what is the part-to-part ratio of girls to boys, and what is the part-to-whole ratio of girls to the total number of students in the class?

The part-to-part ratio of girls to boys is Girls/Boys = 4/3.

The total number of students in the class is 4 + 3 = 7. Thus, the part-to-whole ratio of girls to the total number of students is Girls/Total = 4/7.

So, in general, if we have a part-to-part ratio of A to B, we can say that the corresponding part-to-whole ratios are as follows:

1. A/(A + B)
2. B/(A + B)

Now, let’s discuss solving ratio questions.


In our cat-and-dog example, we calculated that the ratio of cats to dogs was 5 to 6 when there were 11 animals in the room. However, what if we were in a new room with 18 dogs, and we were told that the ratio of cats to dogs was still 5 to 6? Could we determine the number of cats in the new room?