GMAT Ratio and Proportion: Tips, Practice Questions & Answers

Ratio and Proportions are key components of the GMAT Quantitative section, and understanding these concepts can significantly improve your performance. These types of questions are designed to test your ability to compare and relate different quantities, a skill that is crucial for solving a variety of real-world problems. From mixtures to rates and scaling, understanding Ratio and Proportions enables you to approach these problems with ease and efficiency. 

Join us as we explore effective strategies and tips to help you answer Ratio and proportions questions in the GMAT exam.

Understanding the Basics of Ratio and Proportions

Understanding Ratio and Proportions is fundamental to solving many GMAT questions. Let’s break down the key concepts that form the basis for these types of questions.

What is Ratio?

The ratio is the simplest form or comparison of two related numbers. A ratio is a number that expresses one quantity as a fraction of another. For example, the ratio between the integers 5 and 6 is 5:6. It also shows the number of times one quantity equals another. The "terms" refer to the numbers that comprise the ratios. The upper part of the ratio (numerator) is referred to as the antecedent, while the lower part of the proportion (denominator) is known as the consequent or descendent. Ratios can be written in the following forms:

• As a fraction (e.g., ab)
• With a colon (e.g., a:b)

Ratios can also be simplified just like fractions. The simplest form of a ratio is when the two numbers involved have no common factors other than 1.

Example:

If there are 6 boys and 9 girls in a class, the ratio of boys to girls is: 69=2:3

By dividing both the numerator and denominator by 3, we simplify the ratio to its simplest form, which is 2:3.

What is Proportion?

The proportion is represented by the symbols '::' or '='. If the x:y ratio equals the a:b ratio, then x, y, a, and b are proportional. It is represented by the symbols x:y=a:b or x:y: a:b. When four words are proportional, the product of two intermediate values (the second and third) must equal the product of two extremes. A proportion is an equation that states two ratios are equal. This relationship can be expressed in the following form:

ab=cd

Where a, b, c, and d are any numbers. Proportions are used to solve problems involving the comparison of two different quantities. When two ratios are equal, they form a proportion. Proportions can be solved using the cross-multiplication method, where you multiply the numerator of one fraction by the denominator of the other fraction.

Example:

Consider this proportion:

23=x9

To solve for x, we cross-multiply:

29=3x

This simplifies to: 18=3x

Dividing both sides by 3 gives: x=6
So, the missing value x is 6.

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Properties for Ratio and proportions Questions 

Students must consider the following important properties when solving ratio and proportion questions.

GMAT Ratio and proportions Examples 

Ratio and Proportions are essential concepts frequently tested in the GMAT Quantitative section. These questions assess your ability to compare quantities and understand relationships between them. Ratio and proportions problems often involve real-world scenarios, from mixtures and scales to rates and quantities, requiring you to solve for an unknown value. Here are some examples to help you practice and sharpen your understanding of Ratio and Proportions:

1. If 3 boys can complete a task in 12 hours, how many boys are required to complete the task in 8 hours?

Solution: The number of boys needed is inversely proportional to the time taken. So, we can set up the proportion as:

312=x8

Cross-multiply:

38=12x 24=12x

To solve for x, we divide both sides by 12:

x=2

Thus, 2 boys are needed to complete the task in 8 hours.

2. The ratio of the number of apples to oranges in a basket is 5:7. If there are 35 oranges, how many apples are there?

Solution: The ratio of apples to oranges is 5:7, so:

57=a35

Cross-multiply:

535=7a 175=7a

Solving for a, divide both sides by 7:

a=25

Thus, there are 25 apples in the basket.

3. A recipe requires 2 cups of flour for every 3 cups of sugar. How many cups of sugar are needed for 6 cups of flour?

Solution: We can set up the ratio as:

23=6x

Cross-multiply:

2x=36 2x=18

Solving for x, divide both sides by 2:

x=9

Thus, 9 cups of sugar are required.

4. In a group of 240 people, the ratio of males to females is 4:5. How many males are there in the group?

Solution: The total ratio parts are 4+5=9. Now, divide the total number of people by 9 to get the value of one part:

2409=26.67

Now, multiply by 4 (since there are 4 parts for males):

26.674=106.67107

Thus, there are 107 males in the group.

5. A car travels 60 miles in 90 minutes. What is the ratio of distance to time in miles per minute?

Solution: First, convert 90 minutes into hours (since the ratio is typically in miles per hour):

90 minutes=1.5 hours

Now calculate the ratio:

601.5=40 miles per hour

Thus, the ratio of distance to time is 40 miles per hour.

6. The ratio of the number of blue marbles to red marbles in a jar is 3:8. If there are 120 red marbles, how many blue marbles are there?

Solution: We set up the proportion:

38=b120

Cross-multiply:

3120=8b 360=8b

Solving for b, divide both sides by 8:

b=45

Thus, there are 45 blue marbles in the jar.

7. The ratio of students who passed to those who failed in an exam is 3:2. If 180 students passed, how many students failed?

Solution: Let the number of students who failed be f. We can set up the proportion:

32=180f

Cross-multiply:

3f=360

Solving for f, divide both sides by 3:

f=120

Thus, 120 students failed the exam.

8. A teacher has 48 pencils and 72 erasers. What is the ratio of pencils to erasers?

Solution: The ratio of pencils to erasers is:

4872=23

Thus, the ratio of pencils to erasers is 2:3.

9. If a man earns £300 for every 5 hours of work, how much would he earn for 8 hours of work?

Solution: We can set up the proportion:

3005=x8

Cross-multiply:

3008=5x 2400=5x

Solving for x, divide both sides by 5:

x=480

Thus, the man would earn £480 for 8 hours of work.

10. The ratio of the area of two squares is 9:16. If the side length of the first square is 3 metres, what is the side length of the second square?

Solution: The ratio of areas of squares is the square of the ratio of their sides. So, we set up the

proportion:

916=3x2

Taking square roots of both sides:

34=3x

Thus, x=4. So, the side length of the second square is 4 metres.

Certainly! Here are 10 more GMAT-style Ratio and proportions questions with detailed solutions.

11. A bag contains red, blue, and green balls in the ratio of 4:5:6. If there are 120 balls in total, how many blue balls are there?

Solution: The total ratio parts are 4+5+6=15. Now, divide the total number of balls by 15 to find the value of one part:

12015=8

Now, multiply the value of one part by 5 (since there are 5 parts for blue balls):

85=40

Thus, there are 40 blue balls in the bag.

12. A car travels 150 miles in 3 hours. What is the speed of the car in miles per minute?

Solution: First, convert 3 hours into minutes:

3 hours=180 minutes
Now, calculate the speed: 150 miles180 minutes=56 miles per minute
Thus, the car travels at a speed of 56 miles per minute.

13. The ratio of men to women in a workplace is 7:9. If there are 112 men, how many women are there?

Solution: Let the number of women be w. We can set up the proportion:

79=112w

Cross-multiply: 7w=9112 7w=1008
Solving for w, divide both sides by 7:

w=144

Thus, there are 144 women in the workplace.

14. A map has a scale of 1 cm = 5 km. If the distance between two cities on the map is 7 cm, what is the actual distance between the cities?

Solution: Using the scale, we know that 1 cm on the map represents 5 km in reality. Therefore, the actual distance is:

75=35 km

Thus, the actual distance between the cities is 35 km.

15. In a class of 40 students, the ratio of boys to girls is 3:5. How many boys are there in the class?

Solution: The total ratio parts are 3+5=8. Now, divide the total number of students by 8 to find the value of one part:

408=5

Now, multiply the value of one part by 3 (since there are 3 parts for boys):

53=15

Thus, there are 15 boys in the class.

16. A factory produces 500 units of a product in 8 hours. How many units will the factory produce in 10 hours at the same rate?

Solution: We can set up the proportion:

5008=x10

Cross-multiply:

50010=8x 5000=8x

Solving for x, divide both sides by 8:

x=625

Thus, the factory will produce 625 units in 10 hours.

17. The ratio of boys to girls in a group is 7:4. If there are 140 boys, how many girls are there?

Solution: We can set up the proportion:

74=140g

Cross-multiply:

7g=4140 7g=560

Solving for g, divide both sides by 7:

g=80

Thus, there are 80 girls in the group.

18. A recipe calls for 3 cups of flour for every 4 cups of sugar. How many cups of sugar are needed if 9 cups of flour are used?

Solution: We can set up the proportion:

34=9x

Cross-multiply:

3x=49 3x=36

Solving for x, divide both sides by 3:

x=12

Thus, 12 cups of sugar are needed.

19. The ratio of the lengths of two sides of a rectangle is 5:7. If the length of the smaller side is 15 cm, what is the length of the larger side?

Solution: We set up the proportion:

57=15x

Cross-multiply:

5x=715 5x=105

Solving for x, divide both sides by 5:

x=21

Thus, the length of the larger side is 21 cm.

20. In a class of 60 students, the ratio of students who passed to those who failed is 4:1. How many students failed?

Solution: The total ratio parts are 4+1=5. Now, divide the total number of students by 5 to find the value of one part:

605=12

Now, multiply the value of one part by 1 (since there is 1 part for students who failed):

121=12

Thus, 12 students failed the exam.

Strategies to solve GMAT Ratio and proportions questions? 

Ratio and proportions questions are a fundamental part of the GMAT Quantitative section, requiring a clear understanding of relationships between numbers. These problems often appear in various formats, such as word problems, equations, and data interpretation questions. Below are some strategies that will help you approach and solve GMAT Ratio and proportions questions efficiently:

• Identify the type of ratio: Determine whether the problem involves direct or inverse proportions. In direct proportions, as one quantity increases, the other also increases (or decreases in the same manner). In inverse proportions, as one quantity increases, the other decreases.
• Set up a proportion equation: For word problems, clearly define the relationships between the quantities involved. Express the given information as a ratio and use variables for any unknown values.
• Simplify ratios: Simplify ratios to their lowest terms, making calculations quicker and more manageable. Reducing ratios can also help highlight the core relationship between the quantities.
• Use cross-multiplication: If the question provides two ratios that are equal, use the cross-multiplication method to solve for an unknown value.
• Convert to consistent units: Ensure all the quantities involved are in the same units. If the problem involves different units (e.g., time in hours and distance in miles), convert them to a common unit before proceeding.
• Estimate when possible: If the problem involves large numbers or seems complex, use estimation techniques to rule out implausible answer choices and narrow down your options.
• Work backwards if necessary: In problems involving percentages or changes, sometimes working backward from the answer choices can save time and effort.
• Check for proportional relationships: Ensure the quantities are in a consistent, predictable relationship, such as both increasing or decreasing together, or moving in opposite directions.
• Practice different formats: GMAT ratio problems may be presented in different formats, such as word problems, tables, or graphs. Practicing with various types of problems helps you become more adaptable during the exam.
• Break down complex problems: Avoid overcomplicating the problem. Break it down into smaller, more manageable steps to help you focus on the core concepts and solve the problem more effectively.

From the Desk of Yocket

Ratio and Proportions can seem tricky at first, but with the right strategies, they become a lot more manageable. Whether it's a simple direct proportion or a more complex inverse one, understanding the core concepts and practicing regularly can make a significant difference in your GMAT score. Yocket Prep offers expert resources to guide you through such tricky topics and help you build the confidence to tackle the Quantitative section with ease. Make sure you incorporate practice into your study schedule, and soon, solving proportions will be a breeze!