Sec 4 E-Math · Sets

Real-world problems questions with answers

Practice questions on real-world problems, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

In a group of $36$ students, $18$ take the bus to school and $17$ take the MRT to school. $4$ do both. Find the number of students who take the MRT to school only.

Step 1 of 1

Fill the overlap first, then each circle's only part

\mathstrut \text{take the bus to school only} = 18 - 4

\text{take the bus to school only} = 14

\mathstrut \text{take the MRT to school only} = 17 - 4

\text{take the MRT to school only} = 13

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Questions

Question 1Fill the regions
In a group of $50$ students, $12$ play badminton and $9$ play tennis. $4$ do both. Find the number of students who play tennis only.
Show the worked solution
1. Step 1: Fill the overlap first, then each circle's only part $\mathstrut \text{play badminton only} = 12 - 4$ $\text{play badminton only} = 8$ $\mathstrut \text{play tennis only} = 9 - 4$ $\text{play tennis only} = 5$
Question 2Fill the regions
In a group of $45$ people, $25$ own a cat and $14$ own a dog. $7$ do both. Find the number of people who own a dog only.
Show the worked solution
1. Step 1: Fill the overlap first, then each circle's only part $\mathstrut \text{own a cat only} = 25 - 7$ $\text{own a cat only} = 18$ $\mathstrut \text{own a dog only} = 14 - 7$ $\text{own a dog only} = 7$
Question 3Find the overlap
In a group of $36$ people, $18$ own a cat and $14$ own a dog. $5$ do neither. Find the number of people who do both.
Show the worked solution
1. Step 1: Let x be the number who do both. Write each 'only' region in terms of x $\text{own a cat only} = 18 - x$ $\text{own a dog only} = 14 - x$
2. Step 2: The four regions add up to the whole group: write the equation, simplify, solve $(18 - x) + x + (14 - x) + 5 = 36$ $37 - x = 36$ $x = 1$
Question 4Find the overlap
In a group of $30$ people, $18$ own a cat and $17$ own a dog. $5$ do neither. Find the number of people who do both.
Show the worked solution
1. Step 1: Let x be the number who do both. Write each 'only' region in terms of x $\text{own a cat only} = 18 - x$ $\text{own a dog only} = 17 - x$
2. Step 2: The four regions add up to the whole group: write the equation, simplify, solve $(18 - x) + x + (17 - x) + 5 = 30$ $40 - x = 30$ $x = 10$
Question 5Greatest and least overlap
In a group of $30$ members, $25$ swim and $14$ cycle. Find the least possible number of members who do both.
Show the worked solution
1. Step 1: Both groups must fit into the whole group: how many must be counted twice? $\text{Both groups together} = 25 + 14$ $\phantom{\text{Both groups together}} = 39$ $\text{Counted twice} = 39 - 30$ $\text{Least} = 9$
Question 6Greatest and least overlap
In a group of $36$ students, $25$ study French and $17$ study German. Find the greatest possible number of students who do both.
Show the worked solution
1. Step 1: How big can the overlap be? It is inside both groupsThe most is when all 17 of the smaller group do both. $\text{Greatest} = 17$

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Worked example

In a group of

36

students,

18

take the bus to school and

17

take the MRT to school.

4

do both. Find the number of students who take the MRT to school only.

Step 1 of 1

Fill the overlap first, then each circle's only part

\mathstrut \text{take the bus to school only} = 18 - 4

\text{take the bus to school only} = 14

\mathstrut \text{take the MRT to school only} = 17 - 4

\text{take the MRT to school only} = 13

Questions

Question 1Fill the regions

In a group of $50$ students, $12$ play badminton and $9$ play tennis. $4$ do both. Find the number of students who play tennis only.

Show the worked solution

Step 1: Fill the overlap first, then each circle's only part $\mathstrut \text{play badminton only} = 12 - 4$ $\text{play badminton only} = 8$ $\mathstrut \text{play tennis only} = 9 - 4$ $\text{play tennis only} = 5$

Question 2Fill the regions

In a group of $45$ people, $25$ own a cat and $14$ own a dog. $7$ do both. Find the number of people who own a dog only.

Show the worked solution

Step 1: Fill the overlap first, then each circle's only part $\mathstrut \text{own a cat only} = 25 - 7$ $\text{own a cat only} = 18$ $\mathstrut \text{own a dog only} = 14 - 7$ $\text{own a dog only} = 7$

Question 3Find the overlap

In a group of $36$ people, $18$ own a cat and $14$ own a dog. $5$ do neither. Find the number of people who do both.

Show the worked solution

Step 1: Let x be the number who do both. Write each 'only' region in terms of x $\text{own a cat only} = 18 - x$ $\text{own a dog only} = 14 - x$
Step 2: The four regions add up to the whole group: write the equation, simplify, solve $(18 - x) + x + (14 - x) + 5 = 36$ $37 - x = 36$ $x = 1$

Question 4Find the overlap

In a group of $30$ people, $18$ own a cat and $17$ own a dog. $5$ do neither. Find the number of people who do both.

Show the worked solution

Step 1: Let x be the number who do both. Write each 'only' region in terms of x $\text{own a cat only} = 18 - x$ $\text{own a dog only} = 17 - x$
Step 2: The four regions add up to the whole group: write the equation, simplify, solve $(18 - x) + x + (17 - x) + 5 = 30$ $40 - x = 30$ $x = 10$

Question 5Greatest and least overlap

In a group of $30$ members, $25$ swim and $14$ cycle. Find the least possible number of members who do both.

Show the worked solution

Step 1: Both groups must fit into the whole group: how many must be counted twice? $\text{Both groups together} = 25 + 14$ $\phantom{\text{Both groups together}} = 39$ $\text{Counted twice} = 39 - 30$ $\text{Least} = 9$

Question 6Greatest and least overlap

In a group of $36$ students, $25$ study French and $17$ study German. Find the greatest possible number of students who do both.

Show the worked solution

Step 1: How big can the overlap be? It is inside both groupsThe most is when all 17 of the smaller group do both. $\text{Greatest} = 17$