# GRE Arithmetic - Ratios

A **ratio** is a comparison between two numbers, expressed as a division problem. For example, *x* is to *y* is written as *x*/*y*, and this ratio relationship can be stated in one of several ways, including:

*x*to*y*- The ratio of
*x*to*y* *x*is to*y**x*:*y*

Ratio problems can be expressed in one of many ways. On the GRE test, you may be given a math problem that requires you to find a relationship between two stated quantities and then use that relationship to arrive at the answer. For example:

If the ratio of the cost of apples to pears is 30 to 22,

and the cost of an apple is $0.50,

then what is the cost of a pear?

Here's how to solve this problem:

Step 0: | Original Problem | Ratio of cost of apples to pears is 30 to 22, and cost of an apple is $0.50 |

Step 1: | Be sure that you understand the problem. The ratio of the cost of apples to pears does not mean that the cost of 30 apples is equal to the cost of 22 pears. You are told that the ratio of $A/$P = 30/22, where "A" = apples, and "P" = pears. Thus, the cost of 22 apples is equal to 30 pears. First multiply the number of apples by the cost of each apple to get the total cost of 22 apples. | 22×$0.50 = $11.00 |

Step 2: | Because 22 Apples cost as much as 30 Pears, then 30 Pears cost $11.00, so divide $11.00 by 30 to get the cost of each pear. | $11/30 = approximately $0.36 |

The good thing about ratio problems is that you can quickly determine if your answer is correct. In the above example problem, you know that the ratio of the cost of apples to pears is 30 to 22. And, you were told that each apple costs fifty cents. To solve the problem, you calculated that the cost of each pear is approximately 36 cents. Take the ratio of the cost of the two fruits to confirm that your calculation was correct. So, $0.50 to $0.36 is the same as 50/36 = 1.38888, which is the same as 30/22.

Although it's not advised that you double check each solution that you arrive at, you might want to "eyeball" your answer to approximate whether your solution is correct. For example, if you had performed the calculation incorrectly and had concluded that the cost of each pear is 72 cents, then a quick approximation of 50/72 is less than 1. However, the ratio of 30/22 is more than 1, so you'd know right away that your answer is incorrect.