# a total of 100 students play on the sports academy’s soccer, track, or basketball teams. no student plays on more than one team. 61 of the students are boys. there are 36 students on soccer teams, 19 are on the girls’ soccer team. there are 35 students on basketball teams, 18 are on the boys’ basketball team. how many boys are on the track team?

### James

Guys, does anyone know the answer?

get a total of 100 students play on the sports academy’s soccer, track, or basketball teams. no student plays on more than one team. 61 of the students are boys. there are 36 students on soccer teams, 19 are on the girls’ soccer team. there are 35 students on basketball teams, 18 are on the boys’ basketball team. how many boys are on the track team? from EN Bilgi.

## Unit 1 Section 5 : Logic Problems and Venn Diagrams

## Unit 1 Section 5 : Logic Problems and Venn Diagrams

Venn diagrams can be helpful in solving logic problems.

## Example Questions

**Question 1**

In a class there are:

8 students who play football and hockey

7 students who do not play football or hockey

13 students who play hockey

19 students who play football

How many students are there in the class?

We can draw a venn diagram to show the numbers playing football (F) or hockey (H). We can put in the numbers for the first two facts straight away, as seen on the left.

The 8 students who play both hockey and football go in the intersection because they need to be in both circles. The 7 students who don't play either sport go on the outside because they shouldn't be in either circle.

We have to be careful with the other two facts. There are 13 students who play hockey, so the numbers in the hockey circle should add up to 13. We already have 8 in the intersection, so there must be 5 who play hockey but not football. In the same way there are 19 students who play football so the number who play football but not hockey must be 19 – 8 = 11.

To find out the number of students in the class we add up all the sections: 11 + 8 + 5 + 7 = 31

There are 31 students in the class.

**Question 2**

In a class there are 30 students.

21 students like Maths

16 students like English

6 students don't like Maths or English

How many students like both Maths and English?

We can draw a venn diagram to show the numbers who like Maths (M) or English (E), but this time we can only put in a number for one of the facts straight away.

The 6 students who don't like either subject go on the outside because they shouldn't be in either circle. We know the total in the Maths circle needs to be 21 but we can't put this in because we don't know how many should go in the intersection (if they like both subjects) and how many should go on the left (if they only like Maths).

We know there are 30 students in the class, and if there are 6 students outside the circles then the other three sections must add up to 24.

We know there are 21 students who like Maths, so the middle and left section must add up to 21. This leaves 3 on the right because 24 – 21 = 3.

There are 16 students who like English so the two parts of the English circle should add up to 16, so we can find the number in the intersection by doing 16 – 3 = 13.

There are 21 students who like Maths, and 21 – 13 = 8, so the number who like Maths but not English must be 8.

If we check all four facts we were given, we can now see they are all true.

There are 13 students who like both Maths and English.

## Practice Question

Work out the answers to each question part below then click to see whether you are correct.

There are 18 cars on a garage forecourt.

12 cars are diesels.

5 cars are automatics.

3 cars are automatic diesels.

To find out how many cars are not automatic

and not a diesel, work through the stages below.

(a) Where do the 3 automatic diesels get marked on the diagram?

(b) If there are 12 diesels, how many diesels are not automatic?

(c) How many of the automatic cars are not diesels?

(d) How many cars are not automatic and not a diesel?

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

**It may help to have a pencil and paper handy so you can sketch venn diagrams to help you answer the questions.**You have now completed Unit 1 Section 5

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## Making Two

Start studying Making Two-Way Tables Assignment and Quiz 90%. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

## Making Two-Way Tables Assignment and Quiz 90%

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A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. Choose a possible description for the rows and columns.

Column: In a Band, Play a Sport; Row: Not in a Band, Do Not Play a Sport

Column: Not in a Band, Play a Sport; Row: In a Band, Do Not Play a Sport

Column: In a Band, Do Not Play a Sport; Row: Not in a Band, Play a Sport

Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport

Click card to see definition 👆

Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport

Click again to see term 👆

A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table.

Which of the following correctly represents the given data in the problem?

a = 24, g = 48, h = 22, i = 80

a = 22, c = 80, d = 24, i = 48

a = 24, b = 48, c = 22, i = 48

a = 24, c = 48, e = 22, i = 80

Click card to see definition 👆

a = 24, c = 48, e = 22, i = 80

Click again to see term 👆

1/18 Created by claudialems_

### Terms in this set (18)

A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. Choose a possible description for the rows and columns.

Column: In a Band, Play a Sport; Row: Not in a Band, Do Not Play a Sport

Column: Not in a Band, Play a Sport; Row: In a Band, Do Not Play a Sport

Column: In a Band, Do Not Play a Sport; Row: Not in a Band, Play a Sport

Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport

Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport

A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table.

Which of the following correctly represents the given data in the problem?

a = 24, g = 48, h = 22, i = 80

a = 22, c = 80, d = 24, i = 48

a = 24, b = 48, c = 22, i = 48

a = 24, c = 48, e = 22, i = 80

a = 24, c = 48, e = 22, i = 80

A survey of 80 students found that 24 students both play in a band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table.

Determine what each letter in the table should be to complete this two-way table.

b = d = f = g = h = b = 24 d = 10 f = 32 g = 34 h = 46

A summer camp has 32 campers. 22 of them swim, 20 play softball, and 5 do not play softball or swim. Which values correctly complete the table?

a = 15, b = 10, c = 7, d = 5, e = 12

a = 15, b = 7, c = 5, d = 10, e = 12

a = 14, b = 7, c = 5, d = 12, e = 10

a = 14, b = 12, c = 7, d = 5, e = 10

a = 15, b = 7, c = 5, d = 10, e = 12

Partial results of a survey about students who wear glasses are shown in the two-way table.

Which of the following statements are true? Check all that apply.

225 students were surveyed.

25 girls always wear glasses.

15 girls sometimes wear glasses.

52 boys never wear glasses.

75 boys were surveyed.

65 students sometimes wear glasses.

225 students were surveyed.

15 girls sometimes wear glasses.

52 boys never wear glasses.

65 students sometimes wear glasses.

A total of 100 students play on the Sports Academy's soccer, track, or basketball teams. No student plays on more than one team. 61 of the students are boys. There are 36 students on soccer teams, 19 are on the girls' soccer team. There are 35 students on basketball teams, 18 are on the boys' basketball team. How many boys are on the track team?

26

Can you determine what number x represents from the information given? Explain how you got your answer.

Yes, you can determine the number of people who do not run or lift weights by first finding that 55 people do not lift weights, and that 35 people run, but do not lift weights. Subtracting 35 from 55, you get that 20 people do not do either.

Joseph completed the two-way table on the left about the social networking habits of his classmates as follows:

Step 1: 85 - 30 = 55

Step 2: 80 - 55 = 25

Step 3: 140 - 80 = 60

Step 4: 60 - 30 = 30

Step 5: 25 + 30 = 55

The student made no error

Mr. Cho made a two-way table to describe members of his family. Which could describe the row and column headings for Mr. Cho's table?

whether the relative was born in Korea; whether the relative speaks Korean

whether the relative was born in Korea; what their favorite Korean meal is

what city in Korea is their favorite; whether the relative speaks Korean

## Athletics

## Athletics

**About The World Academy Athletics Department**

World Academy athletes are known as NorthStars! Participating in the Tri-County Athletic League affords our athletes opportunities to play and compete with other schools across the State. Heart, pride, strong character, and unwavering sportsmanship are the hallmark for all World Academy student-athletes. It is our hope that during Middle School, students will participate in an athletic sport or club, challenging themselves physically and mentally, while having fun creating memories that will last a lifetime.

Following a seasonal sports schedule allows our athletes to participate in a wide variety of events. Some sports allow for any number of participants, while other teams will have tryouts for limited spots. In the Fall, students can participate in Cross-Country Running and/or Soccer. In the winter months, we offer Basketball, Spirit Team, Volleyball, and Ski Club. Spring showcases Track and Field meets. While these sporting events are team-focused, there are also opportunities for participation without competition, such as skiing in the winter and swimming in the summer. There is a nominal player fee for each sport to defer costs associated with Tri-County dues, referee fees, coaching stipends, travel expenses, and uniforms.

Students are required to attend all practices and scheduled games when part of a team because every team member is of equal importance. Students and parents are kept well informed about when opportunities for tryouts and sign-ups are available. Games, practice, and meet schedules, will be distributed through handouts, emails and the World Academy website. The World Academy website is also the place to track our successes as individuals, teams, and the school as a whole.

In the interest of keeping all of our student-athletes healthy, World Academy strongly encourages all students playing sports in Grades 5-8 to participate in a test called the Immediate Post-Concussion Assessment and Cognitive Testing (imPACT) prior to competing in any sports at the school. This testing will measure memory, processing speed, and reaction time to be kept on file as a baseline score in the event of an injury. If a concussion has occurred, a repeat test can assist in making the decisions about readiness to return to play. Testing can be scheduled at most local hospitals and urgent care clinics. Thank you for helping us keep our student-athletes safe!

In closing, World Academy is happy to announce a new addition to our incredible coaching staff. Aaron Dufoe will be coaching our Girls Soccer and Basketball teams. Mr. Dufoe, a Nashua native, earned undergraduate and graduate degrees in business from Rivier University. Rivier University fostered this talented athlete through an outstanding career in both soccer and basketball, earning multiple accolades. Aaron now dedicates his free time to his wife and children, in addition to coaching female youth soccer and basketball in the greater Nashua area. The expertise of this seasoned coach will bring added value to World Academy Athletics!

Please be sure to check the ‘Athletics’ section of our weekly digital newsletter, Coordinates, for regular updates regarding tryouts, practices, and competitions. For questions, please contact Athletic Director, Erik Congdon at [email protected]

Guys, does anyone know the answer?