# Interpreting Venn diagrams

• 1.

A group of 100 students were asked if they play the piano, the trumpet, or both. The results are shown in the Venn diagram above. Use it to determine the following: the number of students who play piano, the number of students who play trumpet, the number of students who play both, the number of students that play piano or trumpet, and the number of students that do not play either.

• Piano: 65

Trumpet: 40

Piano and Trumpet: 25

Piano or Trumpet: 80

Neither Piano nor Trumpet: 20

• Piano: 65

Trumpet: 40

Piano and Trumpet: 105

Piano or Trumpet: 80

Neither Piano nor Trumpet: 20

• Piano: 40

Trumpet: 15

Piano and Trumpet: 25

Piano or Trumpet: 80

Neither Piano nor Trumpet: 20

• Piano: 65

Trumpet: 40

Piano and Trumpet: 25

Piano or Trumpet: 20

Neither Piano nor Trumpet: 80

• 2.

A group of 50 kids were asked if they like vanilla ice cream, chocolate ice cream, or both. Use the Venn diagram above to find the following: the number of kids who like vanilla, the number of kids who like chocolate, the number of kids who like both, the number of kids that like vanilla or chocolate, and the number of kids that do not like either.

• Vanilla: 10

Chocolate: 25

Vanilla and Chocolate: 10

Vanilla or Chocolate: 45

Neither Vanilla nor Chocolate: 5

• Vanilla: 10

Chocolate: 15

Vanilla and Chocolate: 35

Vanilla or Chocolate: 45

Neither Vanilla nor Chocolate: 5

• Vanilla: 20

Chocolate: 35

Vanilla and Chocolate: 10

Vanilla or Chocolate: 45

Neither Vanilla nor Chocolate: 5

• Vanilla: 20

Chocolate: 35

Vanilla and Chocolate: 55

Vanilla or Chocolate: 45

Neither Vanilla nor Chocolate: 5

• 3.

A group of 80 student athletes were asked if they have played baseball, basketball, or both. Given the Venn diagram above, determine the following: the number of athletes who have played baseball, the number of athletes who have played basketball, the number of athletes who have played both, the number of athletes that have played baseball or basketball, and the number of athletes that have not played either.

• Baseball: 41

• Baseball: 53

• Baseball: 53

• Baseball: 41

• 4.

A group of 120 adults were asked if they like winter, summer, or both seasons. Use the Venn diagram above to find the following: the number of adults who like winter, the number of adults who like summer, the number of adults who like both, the number of adults that like winter or summer, and the number of adults that do not like either.

• Winter: 57

Summer: 50

Winter and Summer: 5

Winter or Summer: 17

Neither Winter nor Summer: 103

• Winter: 53

Summer: 45

Winter and Summer: 5

Winter or Summer: 103

Neither Winter nor Summer: 17

• Winter: 58

Summer: 50

Winter and Summer: 5

Winter or Summer: 103

Neither Winter nor Summer: 17

• Winter: 50

Summer: 58

Winter and Summer: 5

Winter or Summer: 103

Neither Winter nor Summer: 17

• 5.

A group of 150 people were asked if they like actions movies, comedy movies, or both. Look at the Venn diagram above and determine the following: the number who like action movies, the number who like comedy movies, the number who like both, the number that like action or comedy movies, and the number that do not like either.

• Action: 131

Comedy: 89

Action and Comedy: 72

Action or Comedy: 148

Neither Action nor Comedy: 2

• Action: 89

Comedy: 131

Action and Comedy: 72

Action or Comedy: 148

Neither Action nor Comedy: 2

• Action: 17

Comedy: 59

Action and Comedy: 72

Action or Comedy: 148

Neither Action nor Comedy: 2

• Action: 17

Comedy: 59

Action and Comedy: 78

Action or Comedy: 148

Neither Action nor Comedy: 2

• 6.

A group of 60 high school students were asked if they enjoy history, math, or both. Use the Venn diagram above to find the following: the number of students who enjoy history, the number of students who enjoy math, the number of students who enjoy both, the number of students that enjoy history or math, and the number of students that do not enjoy either.

• History: 44

Math: 22

History and Math: 10

History or Math: 56

Neither History nor Math: 4

• History: 44

Math: 22

History and Math: 56

History or Math: 10

Neither History nor Math: 4

• History: 22

Math: 44

History and Math: 10

History or Math: 56

Neither History nor Math: 4

• History: 22

Math: 44

History and Math: 56

History or Math: 10

Neither History nor Math: 4

• 7.

A group of 30 people were asked if they like pepperoni, pineapple, or both toppings on their pizza. Observe the Venn diagram above and determine the following: the number who like pepperoni, the number who like pineapple, the number who like both, the number that like pepperoni or pineapple, and the number that do not like either.

• Pepperoni: 8

Pineapple: 18

Pepperoni and Pineapple: 3

Pepperoni or Pineapple: 23

Neither Pepperoni nor Pineapple: 7

• Pepperoni: 15

Pineapple: 5

Pepperoni and Pineapple: 3

Pepperoni or Pineapple: 23

Neither Pepperoni nor Pineapple: 7

• Pepperoni: 5

Pineapple: 15

Pepperoni and Pineapple: 3

Pepperoni or Pineapple: 23

Neither Pepperoni nor Pineapple: 7

• Pepperoni: 18

Pineapple: 8

Pepperoni and Pineapple: 3

Pepperoni or Pineapple: 23

Neither Pepperoni nor Pineapple: 7

• 8.

A group of 100 adults were asked if they ever broke an arm, a leg, or both. Use the Venn diagram above to find the following: the number of adults who have broken an arm, the number of adults who have broken a leg, the number of adults who have broken both an arm and a leg, the number of adults that have broken an arm or broken a leg, and the number of adults that have never broken either.

• Broken Arm: 51

Broken Leg: 39

Broken Arm and Leg: 35

Broken Arm or Leg: 65

Neither Broken Arm nor Leg: 25

• Broken Arm: 51

Broken Leg: 39

Broken Arm and Leg: 25

Broken Arm or Leg: 35

Neither Broken Arm nor Leg: 65

• Broken Arm: 51

Broken Leg: 39

Broken Arm and Leg: 25

Broken Arm or Leg: 65

Neither Broken Arm nor Leg: 35

• Broken Arm: 51

Broken Leg: 39

Broken Arm and Leg: 65

Broken Arm or Leg: 25

Neither Broken Arm nor Leg: 35

• 9.

A group of 75 adults were asked if they drink coffee, tea, or both. Use the Venn diagram above to find the following: the number of adults who drink coffee, the number of adults who drink tea, the number of adults who drink both, the number of adults that drink coffee or tea, and the number of adults that do not drink either.

• Coffee: 52

Tea: 24

Coffee and Tea: 11

Coffee or Tea: 65

Neither Coffee nor Tea: 10

• Coffee: 24

Tea: 52

Coffee and Tea: 54

Coffee or Tea: 65

Neither Coffee nor Tea: 10

• Coffee: 41

Tea: 13

Coffee and Tea: 54

Coffee or Tea: 65

Neither Coffee nor Tea: 10

• Coffee: 41

Tea: 13

Coffee and Tea: 11

Coffee or Tea: 65

Neither Coffee nor Tea: 10

• 10.

A group of 90 pet owners were asked if they own a dog, a cat, or both. Use the Venn diagram above to find the following: the number who own a dog, the number who own a cat, the number who own both a dog and a cat, the number who own a dog or a cat, and the number who do not own either a dog or a cat.

• Dog: 75

Cat: 65

Dog and Cat: 50

Dog or Cat: 90

Neither Dog nor Cat: 0

• Dog: 75

Cat: 65

Dog and Cat: 50

Dog or Cat: 50

Neither Dog nor Cat: 90

• Dog: 65

Cat: 75

Dog and Cat: 90

Dog or Cat: 50

Neither Dog nor Cat: 0

• Dog: 65

Cat: 75

Dog and Cat: 50

Dog or Cat: 0

Neither Dog nor Cat: 90

• 11.

A group of 200 kids were asked if they like to read, play video games, or do both. Use the Venn diagram above to find the following: the number of kids who like to read, the number of kids who like to play video games, the number of kids who like to do both, the number of kids that like to read or play video games, and the number of kids that do not like to do either.

Video Games: 92

Neither Read nor Video Games: 3

Video Games: 105

Neither Read nor Video Games: 3

Video Games: 105

Neither Read nor Video Games: 197

Video Games: 148

Neither Read nor Video Games: 3

• 12.

A group of 150 athletes were asked if they like to run, bike, or both forms of exercise. Given the Venn diagram above, determine the following: the number of athletes who like to run, the number of athletes who like to bike, the number of athletes who like to do both, the number of athletes that like to run or bike, and the number of athletes that do not like either forms of exercise.

• Run: 111

Bike: 102

Run and Bike: 72

Run or Bike: 141

Neither Run nor Bike: 9

• Run: 39

Bike: 30

Run and Bike: 72

Run or Bike: 141

Neither Run nor Bike: 9

• Run: 72

Bike: 72

Run and Bike: 144

Run or Bike: 141

Neither Run nor Bike: 9

• Run: 111

Bike: 72

Run and Bike: 102

Run or Bike: 9

Neither Run nor Bike: 141

• 13.

A group of 120 adults were asked if they like to vacation at the beach, the mountains, or at both locations. Use the Venn diagram above to find the following: the number of adults who like to go to the beach, the number of adults who like to go to the mountains, the number of adults who like to go to both, the number of adults that like to go to the beach or the mountains, and the number of adults that do not like to go to either locations.

• Beach: 93

Mountains: 38

Beach and Mountains: 12

Beach or Mountains: 119

Neither Beach nor Mountains: 1

• Beach: 38

Mountains: 93

Beach and Mountains: 119

Beach or Mountains: 12

Neither Beach nor Mountains: 1

• Beach: 93

Mountains: 38

Beach and Mountains: 12

Beach or Mountains: 1

Neither Beach nor Mountains: 119

• Beach: 81

Mountains: 26

Beach and Mountains: 107

Beach or Mountains: 119

Neither Beach nor Mountains: 1

• 14.

A group of 50 people were asked if they like to eat hamburgers, hot dogs, or both when at a picnic. From the Venn diagram above, determine the following: the number who like hamburgers, the number who like hot dogs, the number who like both, the number that like hamburgers or hot dogs, and the number that do not like either when at a picnic.

• Hamburger: 21

Hot Dog: 18

Hamburger and Hot Dog: 9

Hamburger or Hot Dog: 2

Neither Hamburger nor Hot Dog: 48

• Hamburger: 27

Hot Dog: 30

Hamburger and Hot Dog: 48

Hamburger or Hot Dog: 9

Neither Hamburger nor Hot Dog: 2

• Hamburger: 30

Hot Dog: 27

Hamburger and Hot Dog: 9

Hamburger or Hot Dog: 48

Neither Hamburger nor Hot Dog: 2

• Hamburger: 9

Hot Dog: 9

Hamburger and Hot Dog: 18

Hamburger or Hot Dog: 48

Neither Hamburger nor Hot Dog: 2

• 15.

A group of 40 college students were asked if they like country music, rock music, or both types of music. The results are shown in the Venn diagram above. Use it to determine the following: the number of students who like country, the number of students who like rock, the number of students who like both, the number of students that like country or rock, and the number of students that do not like either.

• Country: 26

Rock: 26

Country and Rock: 15

Country or Rock: 3

Neither Country nor Rock: 37

• Country: 26

Rock: 26

Country and Rock: 15

Country or Rock: 37

Neither Country nor Rock: 3

• Country: 11

Rock: 11

Country and Rock: 15

Country or Rock: 37

Neither Country nor Rock: 3

• Country: 26

Rock: 26

Country and Rock: 42

Country or Rock: 37

Neither Country nor Rock: 3

• 16.

A group of 200 students were asked if they play the guitar, the drums, or both. The results are shown in the Venn diagram above. Use it to determine the following: the number of students who play the guitar, the number of students who play the drums, the number of students who play both, the number of students that play the guitar or the drums, and the number of students that do not play either.

• Guitar: 130

Drums: 80

Guitar and Drums: 110

Guitar or Drums: 160

Neither Guitar nor Drums: 40

• Guitar: 80

Drums: 30

Guitar and Drums: 50

Guitar or Drums: 160

Neither Guitar nor Drums: 40

• Guitar: 130

Drums: 80

Guitar and Drums: 50

Guitar or Drums: 160

Neither Guitar nor Drums: 40

• Guitar: 130

Drums: 80

Guitar and Drums: 50

Guitar or Drums: 40

Neither Guitar nor Drums: 160

• 17.

A group of 100 kids were asked if they like cake, pie, or both. The results are shown above in the given Venn diagram. Use it to find the following: the number of kids who like cake, the number of kids who like pie, the number of kids who like both, the number of kids who like cake or pie, and the number of kids that do not like either.

• Cake: 40

Pie: 70

Cake and Pie: 20

Cake or Pie: 90

Neither Cake nor Pie: 10

• Cake: 40

Pie: 50

Cake and Pie: 70

Cake or Pie: 90

Neither Cake nor Pie: 10

• Cake: 40

Pie: 70

Cake and Pie: 20

Cake or Pie: 10

Neither Cake nor Pie: 90

• Cake: 20

Pie: 50

Cake and Pie: 20

Cake or Pie: 90

Neither Cake nor Pie: 10

• 18.

A group of 50 student athletes were asked if they have participated in football, track & field, or both. The results are shown in the Venn diagram above. Use it to determine the following: the number of students who participated in football, the number of students who participated in track & field, the number of students who participated in both, the number of students that participated in football or track & field, and the number of students that have not participated in either.

• Football: 23

Track & Field: 31

Football and Track & Field: 5

Football or Track & Field: 49

Neither Football nor Track & Field: 1

• Football: 26

Track & Field: 31

Football and Track & Field: 49

Football or Track & Field: 5

Neither Football nor Track & Field: 1

• Football: 23

Track & Field: 31

Football and Track & Field: 49

Football or Track & Field: 5

Neither Football nor Track & Field: 1

• Football: 18

Track & Field: 26

Football and Track & Field: 5

Football or Track & Field: 49

Neither Football nor Track & Field: 1

• 19.

A group of 150 adults were asked if they like fall, spring, or both. The results are shown in the Venn diagram above. Use it to determine the following: the number of adults who like fall, the number of adults who like spring, the number of adults who like both, the number of adults that like fall or spring, and the number of adults that do not like either season.

• Fall: 67

Spring: 41

Fall and Spring: 39

Fall or Spring: 147

Neither Fall nor Spring: 3

• Fall: 67

Spring: 41

Fall and Spring: 147

Fall or Spring: 39

Neither Fall nor Spring: 3

• Fall: 106

Spring: 80

Fall and Spring: 39

Fall or Spring: 147

Neither Fall nor Spring: 3

• Fall: 106

Spring: 80

Fall and Spring: 147

Fall or Spring: 39

Neither Fall nor Spring: 3

• 20.

A group of 120 people were asked if they watch horror films, romantic films, or both. The results are shown in the Venn diagram above. Use it to determine the following: the number who watch horror films, the number who watch romantic films, the number who watch both, the number that watch horror films or romantic films, and the number that do not watch either genre of films.

• Horror: 21

Romance: 37

Horror and Romance: 11

Horror or Romance: 69

Niether Horror nor Romance: 51

• Horror: 32

Romance: 48

Horror and Romance: 11

Horror or Romance: 69

Niether Horror nor Romance: 51

• Horror: 21

Romance: 37

Horror and Romance: 11

Horror or Romance: 51

Niether Horror nor Romance: 69

• Horror: 32

Romance: 48

Horror and Romance: 69

Horror or Romance: 11

Niether Horror nor Romance: 51

• 21.

A group of 40 elementary school students were asked if they like science class, art class, or both classes. The results are shown in the Venn diagram above. Use it to determine the following: the number of students who like science class, the number of students who like art class, the number of students who like both, the number of students that likes science class or art class, and the number of students that do not like either class.

• Sience: 11

Art: 28

Sience and Art: 29

Science or Art: 5

Neither Science nor Art: 6

• Sience: 5

Art: 28

Sience and Art: 11

Science or Art: 6

Neither Science nor Art: 34

• Sience: 6

Art: 23

Sience and Art: 5

Science or Art: 34

Neither Science nor Art: 6

• Sience: 11

Art: 28

Sience and Art: 5

Science or Art: 34

Neither Science nor Art: 6

• 22.

A group of 20 kids were asked if they like ham, bacon, or both toppings on their pizza. The results are shown above in the given Venn diagram. Use it to find the following: the number of kids who like ham, the number of kids who like bacon, the number of kids who like both toppings, the number of kids who like ham or bacon, and the number of kids that do not like either.

• Ham: 5

Bacon: 16

Ham and Bacon: 3

Ham or Bacon: 18

Neither Ham nor Bacon: 2

• Ham: 2

Bacon: 13

Ham and Bacon: 3

Ham or Bacon: 18

Neither Ham nor Bacon: 2

• Ham: 16

Bacon: 5

Ham and Bacon: 3

Ham or Bacon: 18

Neither Ham nor Bacon: 2

• Ham: 5

Bacon: 16

Ham and Bacon: 3

Ham or Bacon: 2

Neither Ham nor Bacon: 18

• 23.

• Fiction: 24

Nonfiction: 21

Fiction and Nonfiction: 15

Fiction or Nonfiction: 30

Neither Fiction nor Nonfiction: 0

• Fiction: 21

Nonfiction: 24

Fiction and Nonfiction: 15

Fiction or Nonfiction: 30

Neither Fiction nor Nonfiction: 0

• Fiction: 24

Nonfiction: 21

Fiction and Nonfiction: 15

Fiction or Nonfiction: 0

Neither Fiction nor Nonfiction: 30

• Fiction: 24

Nonfiction: 21

Fiction and Nonfiction: 30

Fiction or Nonfiction: 15

Neither Fiction nor Nonfiction: 0

• 24.

A group of 60 adults were asked if they like to drink their coffee black, with cream, or both ways. The results are shown in the Venn diagram above. Use it to determine the following: the number of adults who drink it black, the number of adults who drink it with cream, the number of adults who drink it both ways, the number of adults that drink it black or with cream, and the number of adults that do not drink it either way.

• Black: 36

Cream: 23

Black and Cream: 4

Black or Cream: 55

Neither Black nor Cream: 5

• Black: 32

Cream: 19

Black and Cream: 4

Black or Cream: 55

Neither Black nor Cream: 5

• Black: 19

Cream: 32

Black and Cream: 4

Black or Cream: 55

Neither Black nor Cream: 5

• Black: 23

Cream: 36

Black and Cream: 4

Black or Cream: 55

Neither Black nor Cream: 5

• 25.

A group of 80 kids were asked if they wanted a pet rabbit, hamster, or both. The results are shown above in the given Venn diagram. Use it to find the following: the number of kids who want a rabbit, the number of kids who want a hamster, the number of kids who want both, the number of kids who want a rabbit or a hamster, and the number of kids that do not want either.

• Rabbit: 63

Hamster: 67

Rabbit and Hamster: 60

Rabbit or Hamster: 70

Neither Rabbit nor Hamster: 10

• Rabbit: 67

Hamster: 63

Rabbit and Hamster: 70

Rabbit or Hamster: 60

Neither Rabbit nor Hamster: 10

• Rabbit: 67

Hamster: 63

Rabbit and Hamster: 60

Rabbit or Hamster: 70

Neither Rabbit nor Hamster: 10

• Rabbit: 63

Hamster: 67

Rabbit and Hamster: 70

Rabbit or Hamster: 60

Neither Rabbit nor Hamster: 10

• 26.

• Physical: 37

Audio: 75

Physical and Audio: 12

Physical or Audio: 100

Neither Physical nor Audio: 0

• Physical: 75

Audio: 37

Physical and Audio: 100

Physical or Audio: 12

Neither Physical nor Audio: 0

• Physical: 75

Audio: 37

Physical and Audio: 12

Physical or Audio: 100

Neither Physical nor Audio: 0

• Physical: 63

Audio: 25

Physical and Audio: 12

Physical or Audio: 100

Neither Physical nor Audio: 0

• 27.

A group of 180 people were asked if they like running, swimming, or both. The results are shown in the Venn diagram above. Use it to determine the following: the number who like running, the number who like swimming, the number who like both, the number who like running or swimming, and the number that do not like either forms of exercise.

• Running: 133

Swimming: 122

Running and Swimming: 86

Running or Swimming: 11

Neither Running nor Swimming: 169

• Running: 122

Swimming: 133

Running and Swimming: 169

Running or Swimming: 86

Neither Running nor Swimming: 11

• Running: 47

Swimming: 36

Running and Swimming: 86

Running or Swimming: 169

Neither Running nor Swimming: 11

• Running: 133

Swimming: 122

Running and Swimming: 86

Running or Swimming: 169

Neither Running nor Swimming: 11

• 28.

A group of 140 people were asked if they like to play a board game, watch a move, or both as a fun family activity.. The results are shown in the Venn diagram above. Use it to determine the following: the number who like to play a board game, the number who like to watch a movie, the number who like doing both, the number who like playing board games or watching a movie, and the number that do not like either forms of entertainment.

• Board Game: 89

Movie: 72

Board Game and Movie: 35

Board Game or Movie: 126

Neither Board Game nor Movie: 14

• Board Game: 89

Movie: 72

Board Game and Movie: 125

Board Game or Movie: 14

Neither Board Game nor Movie: 35

• Board Game: 72

Movie: 89

Board Game and Movie: 35

Board Game or Movie: 126

Neither Board Game nor Movie: 14

• Board Game: 89

Movie: 72

Board Game and Movie: 125

Board Game or Movie: 35

Neither Board Game nor Movie: 14

• 29.

A group of 70 kids were asked if they like cheddar cheese chips, sour cream and onion chips, or both types of chips.. The results are shown above in the given Venn diagram. Use it to find the following: the number of kids who like cheese chips, the number of kids who like sour cream and onion chips, the number of kids who like both, the number of kids who like cheddar chips or sour cream and onion chips, and the number of kids that do not like either chip flavor.

• Cheddar: 50

Sour Cream: 51

Cheddar and Sour Cream: 35

Cheddar or Sour Cream: 66

Neither Cheddar nor Sour Cream: 4

• Cheddar: 51

Sour Cream: 50

Cheddar and Sour Cream: 35

Cheddar or Sour Cream: 66

Neither Cheddar nor Sour Cream: 4

• Cheddar: 50

Sour Cream: 51

Cheddar and Sour Cream: 66

Cheddar or Sour Cream: 35

Neither Cheddar nor Sour Cream: 4

• Cheddar: 50

Sour Cream: 51

Cheddar and Sour Cream: 35

Cheddar or Sour Cream: 4

Neither Cheddar nor Sour Cream: 66

• 30.

A group of 90 college students were asked if they like hip-hop, classical, or both types of music. The results are shown in the Venn diagram above. Use it to determine the following: the number of students who like hip-hop, the number of students who like classical music, the number of students who like both genres, the number of students that like hip-hop or classical music, and the number of students that do not like either genre of music.

• Hip-Hop: 60

Classical: 24

Hip-Hop and Classical: 3

Hip-Hop or Classical: 81

Neither Hip-Hop nor Classical: 9

• Hip-Hop: 57

Classical: 21

Hip-Hop and Classical: 3

Hip-Hop or Classical: 9

Neither Hip-Hop nor Classical: 81

• Hip-Hop: 57

Classical: 21

Hip-Hop and Classical: 3

Hip-Hop or Classical: 81

Neither Hip-Hop nor Classical: 9

• Hip-Hop: 60

Classical: 24

Hip-Hop and Classical: 81

Hip-Hop or Classical: 3

Neither Hip-Hop nor Classical: 9

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