02. Frequency Trees

Question 1

$300$ men and women tried to solve a puzzle.

Overall $140$ people did not solve the puzzle.

This information can be seen in the incomplete frequency tree diagram below.

How many women solved the puzzle?

Select the correct answer from the list below:

A: $160$

B: $140$

C: $120$

D: $100$

CORRECT ANSWER:   

WORKED SOLUTION:

Out of the $300$ men and women that tried to solve a puzzle,  $100$ were men thereby $200$ were women.

Of these  $200$ women,  $80$ did not solve the puzzle therefore,

$200-80=120$

So  $120$ women completed the puzzle.

Level 4

Question 2

$300$ men and women tried to solve a puzzle.

Overall $140$ people did not solve the puzzle.

This information can be seen in the incomplete frequency tree diagram below.

How many Men solved the puzzle?

Select the correct answer from the list below:

A: $20$

B: $30$

C: $40$

D: $50$

CORRECT ANSWER:   C: $40$

WORKED SOLUTION:

Given that $80$ women did not complete the puzzle, and the question states that a total $140$ people did not solve the puzzle then,

$140-80=60$

Therefore $60$ men did not solve the puzzle so out of the $100$ men that took part,

$100-60=40$

So $40$ men completed the puzzle.

Level 4

Question 3

$30$ people attended a meeting.

The method by which they arrived and whether they are late or not is summarised in the frequency tree below.

In total $10$ people were late for the meeting.

What fraction of people who cycled to the meeting were on time?

Select the correct answer from the list below:

A: $9$

B: $12$

C: $10$

D: $8$

CORRECT ANSWER:   A: $9$

WORKED SOLUTION:

Out of the $30$ attendees,  $12$ cycled to the meeting.

Of these $12$ women,  $3$ must have been late as the question states that $10$ people were late and $7$ of those walked.

So  $12- 3=9$ people who cycled were on time.

Level 4

Question 4

$30$ people attended a meeting.

The method by which they arrived and whether they are late or not is summarised in the frequency tree below.

In total 12 people were late for the meeting.

How many people who walked to the meeting were on time?

Select the correct answer from the list below:

A: $9$

B: $10$

C: $12$

D: $8$

CORRECT ANSWER:   A: $9$

WORKED SOLUTION:

Out of the $18$ attendees who walked in,  $7$ were late to the meeting.

So that means  $18- 7=9$ people who walked were on time.

Level 4

Question 5

$250$ pupils took part in an end of year test.

Over all $172$ people passed the exam.

This information can be seen in the incomplete frequency tree diagram below.

How many girls failed the exam?

Select the correct answer from the list below:

A: $58$

B: $78$

C: $38$

D: $28$

CORRECT ANSWER:   D: $28$

WORKED SOLUTION:

Out of the $250$ pupils that sat the exam,  $250-172=78$ students failed.

Of these  $72$ students,  $50$ were boys, so there were, $78-50=28$, girls that failed the exam.

Level 4

Question 6

$250$ pupils took part in an end of year test.

Over all $75$ people failed the test.

This information can be seen in the incomplete frequency tree diagram below.

How many girls passed the exam?

Select the correct answer from the list below:

A: $100$

B: $75$

C: $55$

D: $25$

CORRECT ANSWER:   B: $75$

WORKED SOLUTION:

Out of the $250$ pupils that sat the exam,  $250-75=175$ students passed.

Of these $175$ students,  $75$ were boys, so there were, $175-75=100$ girls that passed the exam.

Level 4