What Is Ratios and percents on the GMAT?
Ratios and percents are fundamental tools for expressing relationships and changes in quantities. On the GMAT, they appear in many problem-solving and data-sufficiency questions, often combined with other topics like algebra or word problems. Mastering these concepts is essential for efficient and accurate performance.
Definitions and Core Concepts
A ratio compares two quantities, often written as a fraction (e.g., 2:3) or with the word 'to.' It shows the relative sizes without necessarily giving actual values. A percent is a ratio with a denominator of 100; it expresses a part of a whole as a fraction of 100.
Key terms: part, whole, percent change (increase or decrease), and percent of (e.g., 20% of 50).
Why Ratios and Percents Matter on the GMAT
The GMAT Quantitative section frequently tests proportional reasoning and percentage changes. You'll encounter these in word problems about mixtures, work rates, financial transactions, and data interpretation. Being fluent with ratios and percents allows you to solve these quickly and avoid common traps, especially in data sufficiency where you must assess whether given information is sufficient.
Concrete Example
Suppose a class has boys and girls in a ratio of 3:2. If there are 30 students total, how many boys are there? The ratio means for every 3 boys there are 2 girls, so the total parts are 3+2=5. Each part is 30/5=6 students. Therefore, boys = 3×6 = 18.
For percent change: If a price increases from $50 to $60, the increase is $10. The percent increase is (10/50)×100 = 20%. Note that the base is the original value.
Common Mistakes
- Confusing 'percent increase' with 'percent of.' A 20% increase means the new value is 120% of the original.
- Adding ratios incorrectly: ratios are not additive in the same way as fractions; always find the total parts.
- Forgetting to convert between fractions, decimals, and percents accurately.
- In percent change, using the new value as the base instead of the original.
- Assuming that if two quantities are in a ratio, you know their actual values—you only know relative sizes unless given a total or a difference.
How to Practice
Start by drilling the basics: converting between fractions, decimals, and percents. Then practice setting up ratio equations and solving for unknowns. Use GMAT-style word problems that combine ratios with percentages, such as 'If the ratio of x to y is 3:4 and y is increased by 25%, what is the new ratio?' For data sufficiency, practice identifying what information is needed to answer ratio/percent questions.
Use official GMAT practice questions and timed sets to build speed. Review each mistake to identify whether it was a conceptual error or a calculation slip.