GMAT Ratio and Proportion: Tips, Practice Questions & Answers

Grasping Ratio and Proportions is central to answering numerous GMAT questions. Let us break down the core principles that serve as the foundation for these problem types.

What is a Ratio?

A ratio represents the simplest form or comparison of two related numbers. It is a value that portrays one quantity as a fraction of another. For instance, the ratio between the integers 5 and 6 is given as 5:6. It also indicates how many times one quantity matches another. The numbers making up the ratios are called terms. The top part of the ratio, known as the numerator, is designated as the antecedent, whereas the lower part, known as the denominator, is referred to as the consequent or descendent. Ratios can be formatted in the following ways:

• As a fraction (for example, ab)
• Using a colon (for example, a:b)

Ratios can likewise be reduced just like ordinary fractions. A ratio is in its simplest form when the two numbers involved share no common factors other than 1.

Example:

If a classroom contains 6 boys and 9 girls, the boy-to-girl ratio is expressed as: 69=2:3

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

What is a Proportion?

A proportion is denoted by the symbols '::' or '='. If the ratio x:y equals the ratio a:b, then x, y, a, and b form a proportion. This is written as x:y=a:b or x:y::a:b. When four terms form a proportion, the product of the two inner values (the second and third terms) must equal the product of the two outer values. A proportion is simply an equation showing that two ratios are equal. This relationship can be displayed in the following format:

ab=cd

Here, a, b, c, and d represent any numbers. Proportions are utilized to address problems involving the comparison of two distinct quantities. When a pair of ratios are equal, they create a proportion. Proportions can be solved through cross-multiplication, where you multiply the numerator of one fraction by the denominator of the other fraction.

Example:

Consider the following proportion:

23=x9

To find the value of x, we cross-multiply:

29=3x

This simplifies to: 18=3x

Dividing both sides by 3 yields: x=6Therefore, the missing value x is 6.

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Candidates must keep the following crucial properties in mind when addressing ratio and proportion problems.

Ratio and Proportions are fundamental topics frequently featured in the GMAT Quantitative section. These inquiries test your talent for comparing quantities and understanding the connections between them. Ratio and proportions problems frequently incorporate real-life scenarios, ranging from mixtures and scales to rates and quantities, requiring you to determine an unknown value. Presented below are several examples to help you practice and refine your knowledge of Ratio and Proportions:

1. If 3 boys can finish a job in 12 hours, how many boys are needed to finish the job in 8 hours?

Solution: The quantity of boys required is inversely proportional to the time spent. Hence, we can set up the proportion as follows:

312=x8

Cross-multiply:

38=12x 24=12x

To determine x, we divide both sides by 12:

x=2

Consequently, 2 boys are necessary to finish the job in 8 hours.

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

Solution: Given that the ratio of apples to oranges is 5:7, we write:

57=a35

Cross-multiply:

535=7a 175=7a

To solve for a, divide both sides by 7:

a=25

Therefore, there are 25 apples present in the basket.

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

Solution: We can structure the ratio in this manner:

23=6x

Cross-multiply:

2x=36 2x=18

To solve for x, divide both sides by 2:

x=9

Thus, 9 cups of sugar are needed.

4. Within a group of 240 individuals, the ratio of males to females is 4:5. How many males belong to this group?

Solution: The aggregate ratio units equal 4+5=9. Next, divide the total count of people by 9 to discover the value of a single unit:

2409=26.67

Now, multiply this by 4 (since males account for 4 units):

26.674=106.67107

As a result, there are 107 males in the group.

5. An automobile travels 60 miles in 90 minutes. What is the ratio of distance to time expressed in miles per minute?

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

90 minutes=1.5 hours

Now compute the ratio:

601.5=40 miles per hour

Therefore, the distance-to-time ratio is 40 miles per hour.

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

Solution: We formulate the proportion:

38=b120

Cross-multiply:

3120=8b 360=8b

To solve for b, divide both sides by 8:

b=45

Consequently, there are 45 blue marbles in the jar.

7. The ratio of passing students to failing students on a test is 3:2. If 180 students passed, how many students failed?

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

32=180f

Cross-multiply:

3f=360

To find f, divide both sides by 3:

f=120

Thus, 120 students failed the test.

8. An instructor owns 48 pencils and 72 erasers. Find the ratio of pencils to erasers.

Solution: The ratio of pencils to erasers is expressed as:

4872=23

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

9. If a worker makes £300 for every 5 hours worked, what will be their earnings for 8 hours of work?

Solution: We can formulate the proportion:

3005=x8

Perform cross-multiplication:

3008=5x 2400=5x

To solve for x, divide both sides by 5:

x=480

Hence, the worker would earn £480 for 8 hours of work.

10. The ratio of the areas of two squares is 9:16. Given that the side length of the initial square is 3 metres, determine the side length of the second square.

Solution: The ratio between the areas of squares equals the square of the ratio of their side lengths. Thus, we write the

proportion:

916=3x2

Extract the square root of both sides:

34=3x

Consequently, x=4. Therefore, the side length of the second square is 4 metres.

Certainly! Here are 10 additional GMAT-style Ratio and proportions problems complete with step-by-step solutions.

11. A container holds red, blue, and green spheres in a 4:5:6 ratio. If the total number of spheres is 120, how many blue spheres are present?

Solution: The sum of the ratio parts is 4+5+6=15. Next, divide the total number of spheres by 15 to determine the value of a single part:

12015=8

Now, multiply the value of one part by 5 (since blue spheres correspond to 5 parts):

85=40

Thus, there are 40 blue spheres inside the container.

12. An automobile drives 150 miles in 3 hours. What is the car velocity measured in miles per minute?

Solution: Initially, convert 3 hours into minutes:

3 hours=180 minutesNext, determine the velocity: 150 miles180 minutes=56 miles per minuteThus, the automobile travels at a velocity of 56 miles per minute.

13. The proportion of male employees to female employees at an office is 7:9. If there are 112 men, how many women are employed there?

Solution: Let w represent the number of women. We can establish the proportion:

79=112w

Perform cross-multiplication: 7w=9112 7w=1008To isolate w, divide both sides by 7:

w=144

Consequently, there are 144 women at the office.

14. A geographical map uses a scale of 1 cm = 5 km. If two locations are separated by 7 cm on this map, what is the actual distance separating them?

Solution: Based on the scale, 1 cm on the map corresponds to 5 km in the physical world. Hence, the true distance is:

75=35 km

Therefore, the actual distance between the two locations is 35 km.

15. Within a classroom of 40 pupils, the ratio of boys to girls stands at 3:5. How many boys are enrolled in this class?

Solution: The total ratio parts add up to 3+5=8. Next, divide the total pupil count by 8 to find the value of a single part:

408=5

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

53=15

Thus, there are 15 boys in the classroom.

16. A manufacturing plant makes 500 items in 8 hours. How many items will the plant manufacture in 10 hours maintaining the same pace?

Solution: We can set up the following proportion:

5008=x10

Perform cross-multiplication:

50010=8x 5000=8x

To solve for x, divide both sides by 8:

x=625

Hence, the plant will manufacture 625 items over 10 hours.

17. The ratio of boys to girls in a specific gathering is 7:4. Given that there are 140 boys, how many girls are present?

Solution: We can formulate the proportion:

74=140g

Perform cross-multiplication:

7g=4140 7g=560

To isolate g, divide both sides by 7:

g=80

Therefore, there are 80 girls in the gathering.

18. A culinary recipe requires 3 measures of flour for every 4 measures of sugar. How many measures of sugar are needed if 9 measures of flour are utilized?

Solution: We can establish the proportion:

34=9x

Perform cross-multiplication:

3x=49 3x=36

To solve for x, divide both sides by 3:

x=12

Thus, 12 measures of sugar are required.

19. The ratio between the lengths of two adjacent sides of a rectangular shape is 5:7. If the shorter side measures 15 cm, what is the length of the longer side?

Solution: We construct the proportion:

57=15x

Perform cross-multiplication:

5x=715 5x=105

To find x, divide both sides by 5:

x=21

Hence, the longer side measures 21 cm in length.

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

Solution: The aggregate ratio components are 4+1=5. Now, divide the total number of learners by 5 to determine the value of one part:

605=12

Next, multiply the value of one part by 1 (since the failing learners correspond to 1 part):

121=12

Therefore, 12 learners failed the test.

Ratio and proportions problems constitute an essential component of the GMAT Quantitative section, demanding a solid grasp of numerical associations. These inquiries frequently manifest in diverse formats, including word problems, algebraic equations, and data analysis tasks. Presented below are several techniques to assist you in tackling and solving GMAT Ratio and proportions problems effectively:

• Recognize the ratio category: Ascertain whether the problem entails direct or inverse proportions. In direct proportions, as one metric rises, the other rises as well (or falls correspondingly). In inverse proportions, as one metric rises, the other falls.
• Establish a proportional equation: For verbal problems, explicitly outline the connections among the relevant quantities. Translate the provided data into a ratio format and assign variables to any unknown figures.
• Reduce ratios: Simplify ratios down to their simplest form to render computations faster and simpler. Reducing ratios also helps underscore the fundamental association between quantities.
• Apply cross-multiplication: When a problem presents two identical ratios, utilize the cross-multiplication technique to determine an unknown quantity.
• Standardize units: Verify that all quantities involved share identical units. If a problem incorporates mixed units (such as duration in hours and length in miles), convert them into a uniform unit before moving forward.
• Estimate whenever feasible: When a problem features large figures or appears overly complicated, apply approximation methods to eliminate unreasonable answer options and narrow your choices.
• Work in reverse if necessary: For problems involving percentages or alterations, occasionally starting backward from the provided answers can preserve time and energy.
• Verify proportional consistency: Confirm that the quantities maintain a steady, predictable dynamic, such as both increasing or decreasing concurrently, or progressing in opposing directions.
• Work with various formats: GMAT ratio questions can appear in multiple styles, including graphs, tables, and word problems. Training on diverse question types builds your flexibility for the test.
• Simplify intricate questions: Refrain from making the problem overly complicated. Divide it into bite-sized, manageable parts so you can concentrate on the fundamental principles and reach the answer more efficiently.