Mastering Ratios and Proportions for GRE Quantitative Reasoning
Ratios and proportions are fundamental concepts in quantitative reasoning, frequently appearing in various forms on the GRE. Understanding how to set up, manipulate, and solve problems involving these concepts is crucial for achieving a high score. This module will break down ratios and proportions, providing you with the knowledge and practice needed to tackle these questions confidently.
Understanding Ratios
A ratio is a comparison of two or more quantities. It tells us how much of one thing there is compared to another. Ratios can be expressed in several ways:
It's important to maintain the order of the quantities when expressing a ratio. If the ratio of boys to girls is 5:3, it means for every 5 boys, there are 3 girls. The ratio of girls to boys would be 3:5.
The ratio of boys to girls is 12:18, which can be simplified to 2:3.
Simplifying Ratios
Like fractions, ratios can often be simplified by dividing both parts of the ratio by their greatest common divisor (GCD). For example, the ratio 12:18 can be simplified by dividing both numbers by 6, resulting in 2:3.
Simplifying ratios is key to making calculations easier and identifying underlying relationships.
Understanding Proportions
A proportion is an equation stating that two ratios are equal. For instance, if the ratio of boys to girls in one class is 2:3, and in another class it's 4:6, these two ratios form a proportion because they represent the same relative relationship. We can write this as 2/3 = 4/6.
In a proportion a/b = c/d, the terms 'a' and 'd' are called the extremes, and the terms 'b' and 'c' are called the means. A fundamental property of proportions is that the product of the means equals the product of the extremes (ad = bc). This is often referred to as the "cross-multiplication" rule.
Consider a proportion where the ratio of apples to oranges is 2:3. If you have 6 apples, how many oranges do you have? We can set up the proportion: 2/3 = 6/x. Using cross-multiplication, we get 2 * x = 3 * 6, which simplifies to 2x = 18. Dividing both sides by 2 gives x = 9. Therefore, you have 9 oranges. This visual demonstrates how setting up the proportion and applying the cross-multiplication rule allows us to solve for an unknown quantity.
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Solving Ratio and Proportion Problems
GRE problems often involve scenarios where you need to find an unknown quantity given a ratio or a proportion. The key is to:
Set up the proportion: 5 shirts / 120.
Advanced Ratio Concepts
Some GRE problems involve combined ratios or ratios of three or more quantities. For example, if the ratio of A to B is 2:3 and the ratio of B to C is 4:5, you need to make the 'B' part of both ratios the same to find the ratio of A to C. You can do this by finding a common multiple for B (which is 12 in this case). Multiply the first ratio by 4 (giving 8:12) and the second by 3 (giving 12:15). Now, the ratio of A:B:C is 8:12:15.
| Concept | Description | Example |
|---|---|---|
| Ratio | Comparison of two or more quantities. | Boys to Girls = 2:3 |
| Proportion | Equality of two ratios. | 2/3 = 4/6 |
| Cross-Multiplication | Product of means equals product of extremes (ad=bc). | In 2/3 = 4/6, 26 = 34 |
| Combined Ratio | Finding a single ratio from multiple related ratios. | A:B = 2:3, B:C = 4:5 => A:B:C = 8:12:15 |
Practice Strategies
To excel in ratio and proportion questions on the GRE, consistent practice is key. Focus on:
Don't just memorize formulas; understand the underlying logic of ratios and proportions. This will help you adapt to different problem variations.
Learning Resources
Official GRE study material from ETS, providing a concise overview and practice questions for ratios and proportions.
Comprehensive video lessons and practice exercises covering the fundamentals of ratios, proportions, and their applications.
A detailed blog post from Magoosh explaining common GRE ratio and proportion question types and strategies.
Kaplan's guide to understanding and solving ratio and proportion problems, with tips for the GRE.
A comprehensive video tutorial covering various aspects of ratios and proportions relevant to the GRE exam.
An in-depth article from Manhattan Prep that breaks down these related concepts and provides strategic advice for GRE questions.
Free resources from GregMat+ including explanations and practice problems specifically tailored for GRE ratios and proportions.
A focused tutorial on ratios with practice questions and explanations designed for GRE preparation.
A user-friendly explanation of ratios and proportions with interactive examples and clear definitions.
Community discussions and solved problems related to ratios and proportions, offering insights into common GRE question patterns and solutions.