Work Distribution - CCAT Test Prep

This type of question tests your understanding of overlapping sets and logical relationships among groups. Such problems often involve employees with multiple roles or overlapping skills, and solving them requires careful tracking of individuals working in different areas. To solve these problems, break down the information logically, and use simple addition or subtraction.

How to Solve Overlapping Set Questions

Question 1 - Overlapping Employee Roles

In a retail store with 36 employees, 29 work with customers, 11 work in the warehouse, and 4 do neither. How many employees both work with customers and work in the warehouse?

A) 3
B) 4
C) 6
D) 8
E) 11

Understand the Problem:

We are given information about different groups of employees:

Total employees: 36
Work with customers: 29
Work in the warehouse: 11
Do neither: 4

Breakdown the Information:

Since 4 employees do neither, the rest (i.e., 36 - 4 = 32) are either working with customers, in the warehouse, or both.
We know 29 employees work with customers, and 11 work in the warehouse. Let’s denote those working in both areas as X.

Setting up the Equation:

To find the overlapping value, let's add the groups:

Employees working with customers + Employees working in the warehouse - Overlapping employees = Total employees working in any capacity.

29 + 11 - X = 32

Solve for X:

40 - X = 32

X = 8

Answer: 8

By breaking down the problem step by step and using simple logic, you can quickly determine the correct answer without making the process complicated.

Question 2 - Distribution of Tasks

A team of 50 people is working on two projects. Thirty-five people are working on Project A, twenty-five people are working on Project B, and ten people are not involved in either project. How many people are working on both Project A and Project B?

A) 5
B) 10
C) 15
D) 20
E) 25

Understand the Problem:

Total team members: 50
Working on Project A: 35
Working on Project B: 25
Not involved in either project: 10

Breakdown:

40 team members are involved in at least one project (50 - 10).
Let X be the number of people working on both projects.

Set up the Equation:

35 + 25 - X = 40

Solve for X:

60 - X = 40

X = 20

Answer: 20

Question 3 - Overlapping Study Groups

In a study group of 45 students, 30 are learning Python, 20 are learning Java, and 10 are learning neither. How many students are learning both Python and Java?

A) 5
B) 10
C) 15
D) 20
E) 25

Understand the Problem:

Total students: 45
Learning Python: 30
Learning Java: 20
Learning neither: 10

Breakdown:

35 students are involved in at least one language (45 - 10).
Let X be the number of students learning both languages.

Set up the Equation:

30 + 20 - X = 35

Solve for X:

50 - X = 35

X = 15

Answer: 15

How to Solve These Questions Easily

Identify Groups:

Identify the different groups involved and the total number of individuals. Remember to subtract those not involved to get the relevant numbers.

Use an Overlapping Formula:

Use the equation:

(Total in Group A) + (Total in Group B) - (Total in Both Groups) = (Total in At Least One Group)

Solve for the Overlap:

Solve for the value representing the overlap. This simple approach keeps your calculations organized and reduces the chance of errors.

Certainly! Here are the recalculated answers along with step-by-step explanations for each question:

20 Practice Questions with Anwsers

A class of 60 students includes 40 who are taking math, 30 who are taking science, and 15 who are taking neither subject. How many students are taking both math and science?

Total Students = 60
Students taking neither = 15
Students taking at least one subject = 60 - 15 = 45
Math only + Science only + Both = 45
Math + Both = 40
Science + Both = 30
To find the number of students taking both:

  Math + Science - Both = 45
  40 + 30 - Both = 45
  70 - Both = 45
  Both = 70 - 45 = 25

Answer: 25

In an office of 100 employees, 70 have access to email, 50 have access to the internal chat system, and 20 have neither. How many have access to both?

Total Employees = 100
Employees with neither = 20
Employees with at least one access = 100 - 20 = 80
Email only + Chat only + Both = 80
Email + Both = 70
Chat + Both = 50
To find the number of employees with both:

  Email + Chat - Both = 80
  70 + 50 - Both = 80
  120 - Both = 80
  Both = 120 - 80 = 40

Answer: 40

A community center has 80 members, 60 participate in yoga, 50 participate in dance, and 30 do neither. How many members participate in both activities?

Total Members = 80
Members doing neither = 30
Members doing at least one activity = 80 - 30 = 50
Yoga + Dance - Both = 50
Yoga + Both = 60
Dance + Both = 50
To find the number of members doing both:

  Yoga + Dance - Both = 50
  60 + 50 - Both = 50
  110 - Both = 50
  Both = 110 - 50 = 60

Answer: 60

Of the 120 people at a conference, 70 attended Workshop A, 80 attended Workshop B, and 30 attended neither. How many attended both workshops?

Total People = 120
People attending neither = 30
People attending at least one workshop = 120 - 30 = 90
Workshop A + Workshop B - Both = 90
Workshop A + Both = 70
Workshop B + Both = 80
To find the number attending both workshops:

  Workshop A + Workshop B - Both = 90
  70 + 80 - Both = 90
  150 - Both = 90
  Both = 150 - 90 = 60

Answer: 60

In a gym with 90 members, 60 use the treadmill, 40 use the weights, and 20 use neither. How many use both the treadmill and weights?

Total Members = 90
Members using neither = 20
Members using at least one equipment = 90 - 20 = 70
Treadmill + Weights - Both = 70
Treadmill + Both = 60
Weights + Both = 40
To find the number using both:

  Treadmill + Weights - Both = 70
  60 + 40 - Both = 70
  100 - Both = 70
  Both = 100 - 70 = 30

Answer: 30

In a group of 50 employees, 35 have attended safety training, 25 have attended communication skills training, and 10 have attended neither. How many employees have attended both types of training?

Total Employees = 50
Employees with neither training = 10
Employees with at least one training = 50 - 10 = 40
Safety Training + Communication Training - Both = 40
Safety Training + Both = 35
Communication Training + Both = 25
To find the number attending both:

  Safety + Communication - Both = 40
  35 + 25 - Both = 40
  60 - Both = 40
  Both = 60 - 40 = 20

Answer: 20

A total of 100 people are at a concert. Seventy-five enjoy rock music, 50 enjoy jazz, and 15 enjoy neither. How many enjoy both rock and jazz?

Total People = 100
People enjoying neither = 15
People enjoying at least one genre = 100 - 15 = 85
Rock + Jazz - Both = 85
Rock + Both = 75
Jazz + Both = 50
To find the number enjoying both:

  Rock + Jazz - Both = 85
  75 + 50 - Both = 85
  125 - Both = 85
  Both = 125 - 85 = 40

Answer: 40

In a group of 70 students, 50 study English, 40 study History, and 20 study neither. How many students study both subjects?

Total Students = 70
Students studying neither = 20
Students studying at least one subject = 70 - 20 = 50
English + History - Both = 50
English + Both = 50
History + Both = 40
To find the number studying both:

  English + History - Both = 50
  50 + 40 - Both = 50
  90 - Both = 50
  Both = 90 - 50 = 40

Answer: 40

Continuing with the step-by-step explanations for the remaining 12 questions:

Out of 150 employees in a company, 80 work in sales, 90 work in marketing, and 30 work in neither. How many work in both departments?

Total Employees = 150
Employees working in neither department = 30
Employees working in at least one department = 150 - 30 = 120
Sales + Marketing - Both = 120
Sales + Both = 80
Marketing + Both = 90
To find the number working in both:

  Sales + Marketing - Both = 120
  80 + 90 - Both = 120
  170 - Both = 120
  Both = 170 - 120 = 50

Answer: 50

A club has 200 members. One hundred and twenty are interested in cycling, 100 are interested in running, and 50 are interested in neither. How many are interested in both cycling and running?

Total Members = 200
Members interested in neither = 50
Members interested in at least one activity = 200 - 50 = 150
Cycling + Running - Both = 150
Cycling + Both = 120
Running + Both = 100
To find the number interested in both:

  Cycling + Running - Both = 150
  120 + 100 - Both = 150
  220 - Both = 150
  Both = 220 - 150 = 70

Answer: 70

In a school of 300 students, 200 play football, 150 play basketball, and 80 play neither. How many students play both sports?

Total Students = 300
Students playing neither = 80
Students playing at least one sport = 300 - 80 = 220
Football + Basketball - Both = 220
Football + Both = 200
Basketball + Both = 150
To find the number playing both:

  Football + Basketball - Both = 220
  200 + 150 - Both = 220
  350 - Both = 220
  Both = 350 - 220 = 130

Answer: 130

A survey of 1000 people found that 700 like tea, 500 like coffee, and 300 like neither. How many like both tea and coffee?

Total People = 1000
People liking neither = 300
People liking at least one drink = 1000 - 300 = 700
Tea + Coffee - Both = 700
Tea + Both = 700
Coffee + Both = 500
To find the number liking both:

  Tea + Coffee - Both = 700
  700 + 500 - Both = 700
  1200 - Both = 700
  Both = 1200 - 700 = 500

Answer: 500

In a class of 80 students, 55 are learning French, 45 are learning Spanish, and 20 are learning neither. How many are learning both languages?

Total Students = 80
Students learning neither = 20
Students learning at least one language = 80 - 20 = 60
French + Spanish - Both = 60
French + Both = 55
Spanish + Both = 45
To find the number learning both:

  French + Spanish - Both = 60
  55 + 45 - Both = 60
  100 - Both = 60
  Both = 100 - 60 = 40

Answer: 40

A company of 150 employees has 90 who work in software, 70 who work in hardware, and 40 who do neither. How many work in both departments?

Total Employees = 150
Employees working in neither = 40
Employees working in at least one department = 150 - 40 = 110
Software + Hardware - Both = 110
Software + Both = 90
Hardware + Both = 70
To find the number working in both:

  Software + Hardware - Both = 110
  90 + 70 - Both = 110
  160 - Both = 110
  Both = 160 - 110 = 50

Answer: 50

In a community of 500 people, 300 speak English, 250 speak Spanish, and 100 speak neither. How many people speak both languages?

Total People = 500
People speaking neither = 100
People speaking at least one language = 500 - 100 = 400
English + Spanish - Both = 400
English + Both = 300
Spanish + Both = 250
To find the number speaking both:

  English + Spanish - Both = 400
  300 + 250 - Both = 400
  550 - Both = 400
  Both = 550 - 400 = 150

Answer: 150

A market survey indicates that 70 people like Product A, 60 like Product B, and 20 dislike both products. If there are 100 people surveyed, how many like both Product A and B?

Total People = 100
People disliking both products = 20
People liking at least one product = 100 - 20 = 80
Product A + Product B - Both = 80
Product A + Both = 70
Product B + Both = 60
To find the number liking both:

  Product A + Product B - Both = 80
  70 + 60 - Both = 80
  130 - Both = 80
  Both = 130 - 80 = 50

Answer: 50

Out of 500 employees, 350 use public transport, 200 drive cars, and 100 use neither. How many use both modes of transport?

Total Employees = 500
Employees using neither = 100
Employees using at least one mode = 500 - 100 = 400
Public Transport + Cars - Both = 400
Public Transport + Both = 350
Cars + Both = 200
To find the number using both:

  Public Transport + Cars - Both = 400
  350 + 200 - Both = 400
  550 - Both = 400
  Both = 550 - 400 = 150

Answer: 150

A hotel survey finds that 180 guests prefer vegetarian food, 120 prefer vegan food, and 50 prefer neither. Out of 300 guests, how many prefer both vegetarian and vegan food?

Total Guests = 300
Guests preferring neither = 50
Guests preferring at least one type of food = 300 - 50 = 250
Vegetarian + Vegan - Both = 250
Vegetarian + Both = 180
Vegan + Both = 120
To find the number preferring both:

  Vegetarian + Vegan - Both = 250
  180 + 120 - Both = 250
  300 - Both = 250
  Both = 300 - 250 = 50

Answer: 50

In a group of 60 people, 40 enjoy swimming, 30 enjoy hiking, and 10 enjoy neither activity. How many enjoy both swimming and hiking?

Total People = 60
People enjoying neither = 10
People enjoying at least one activity = 60 - 10 = 50
Swimming + Hiking - Both = 50
Swimming + Both = 40
Hiking + Both = 30
To find the number enjoying both:

  Swimming + Hiking - Both = 50
  40 + 30 - Both = 50
  70 - Both = 50
  Both = 70 - 50 = 20

Answer: 20

In a factory, 300 workers are employed. Two hundred work in production, 150 work in quality control, and 80 do neither. How many workers are involved in both areas?

Total Workers = 300
Workers doing neither = 80
Workers involved in at least one area = 300 - 80 = 220
Production + Quality Control - Both = 220
Production + Both = 200
Quality Control + Both = 150
To find the number working in both:

  Production + Quality Control - Both = 220
  200 + 150 - Both = 220
  350 - Both = 220
  Both = 350 - 220 = 130

Answer: 130

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