Number_gap-2026_667

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

667

Question

60% of students at a university are undergraduates. 50% of undergraduates are studying science. 20% of undergraduate science students are in their final year.

What percentage of university students are final year undergraduate science students?

Worked Solution
Undergraduates = 60% of all students

Undergraduate science students = 50% of 60%
= 30% of all students

Final year undergraduate science students = 20% of 30%
= 6%

∴\therefore 6% of university students are final year undergraduate science students.

Question Type

Answer Box

Variables

Variable nameVariable value
question
60% of students at a university are undergraduates. 50% of undergraduates are studying science. 20% of undergraduate science students are in their final year. What percentage of university students are final year undergraduate science students?
workedSolution
| | | | ----------------------:| ---------------------------- | | Undergraduates | \= 60% of all students |

| | | | --------------------------------:| ---------------------------- | | Undergraduate science students | \= 50% of 60% | | | \= 30% of all students |

| | | | -------------------------------------------:| ---------------------------------------- | | Final year undergraduate science students | \= 20% of 30% | | | \= {{{correctAnswer0}}}% |

$\therefore$ {{{correctAnswer0}}}% of university students are final year undergraduate science students.
correctAnswer0
6
prefix0
suffix0
%

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer06

%

Variant 1

DifficultyLevel

668

Question

80% of members at a sports club are adults. 25% of adult members play tennis. 30% of adult tennis players compete in tournaments.

What percentage of all members are adults who compete in tennis tournaments?

Worked Solution
Adult members = 80% of all members

Adult tennis players = 25% of 80%
= 20% of all members

Adults competing in tennis tournaments = 30% of 20%
= 6%

∴\therefore 6% of all members are adults who compete in tennis tournaments.

Question Type

Answer Box

Variables

Variable nameVariable value
question
80% of members at a sports club are adults. 25% of adult members play tennis. 30% of adult tennis players compete in tournaments. What percentage of all members are adults who compete in tennis tournaments?
workedSolution
| | | | ----------------------------:| ---------------------------- | | Adult members | \= 80% of all members |

| | | | ----------------------------:| ---------------------------- | | Adult tennis players | \= 25% of 80% | | | \= 20% of all members |

| | | | -----------------------------------------:| ---------------------------- | | Adults competing in tennis tournaments | \= 30% of 20% | | | \= {{{correctAnswer0}}}% |

$\therefore$ {{{correctAnswer0}}}% of all members are adults who compete in tennis tournaments.
correctAnswer0
6
prefix0
suffix0
%

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer06

%

Variant 2

DifficultyLevel

667

Question

75% of employees at a company work full time. 40% of full time employees work in sales. 20% of full time sales employees are female. 25% of full time female sales employees are managers.

What percentage of all employees are full time female sales managers?

Worked Solution
Full time employees = 75% of all employees

Full time sales employees = 40% of 75%
= 30% of all employees

Full time female sales employees = 20% of 30%
= 6% of all employees

Full time female sales managers = 25% of 6%
= 1.5%

∴\therefore 1.5% of all employees are full time female sales managers.

Question Type

Answer Box

Variables

Variable nameVariable value
question
75% of employees at a company work full time. 40% of full time employees work in sales. 20% of full time sales employees are female. 25% of full time female sales employees are managers. What percentage of all employees are full time female sales managers?
workedSolution
| | | | ----------------------------:| ---------------------------- | | Full time employees | \= 75% of all employees |

| | | | ----------------------------:| ---------------------------- | | Full time sales employees | \= 40% of 75% | | | \= 30% of all employees |

| | | | ----------------------------------:| ---------------------------- | | Full time female sales employees | \= 20% of 30% | | | \= 6% of all employees |

| | | | -------------------------------------------:| ---------------------------- | | Full time female sales managers | \= 25% of 6% | | | \= {{{correctAnswer0}}}% |

$\therefore$ {{{correctAnswer0}}}% of all employees are full time female sales managers.
correctAnswer0
1.5
prefix0
suffix0
%

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer01.5

%

Variant 3

DifficultyLevel

669

Question

60% of people in a town own a car. 45% of car owners also own a bicycle. 20% of those who own both a car and bicycle use both to commute. 50% of those commuters are female.

What percentage of all people in the town are females who commute using both a car and bicycle?

Worked Solution
Car owners = 60% of all people

Car and bicycle owners = 45% of 60%
= 27% of all people

Car and bicycle commuters = 20% of 27%
= 5.4% of all people

Female car and bicycle commuters = 50% of 5.4%
= 2.7%

∴\therefore 2.7% of all people in the town are females who commute using both a car and bicycle.

Question Type

Answer Box

Variables

Variable nameVariable value
question
60% of people in a town own a car. 45% of car owners also own a bicycle. 20% of those who own both a car and bicycle use both to commute. 50% of those commuters are female. What percentage of all people in the town are females who commute using both a car and bicycle?
workedSolution
| | | | ----------------------------:| ---------------------------- | | Car owners | \= 60% of all people |

| | | | ----------------------------:| ---------------------------- | | Car and bicycle owners | \= 45% of 60% | | | \= 27% of all people |

| | | | -----------------------------------------:| ---------------------------- | | Car and bicycle commuters | \= 20% of 27% | | | \= 5.4% of all people |

| | | | -----------------------------------------:| ---------------------------- | | Female car and bicycle commuters | \= 50% of 5.4% | | | \= {{{correctAnswer0}}}% |

$\therefore$ {{{correctAnswer0}}}% of all people in the town are females who commute using both a car and bicycle.
correctAnswer0
2.7
prefix0
suffix0
%

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer02.7

%

Variant 4

DifficultyLevel

671

Question

70% of students at a school study a language. 40% of language students study French. 25% of French students also study Spanish. 20% of those studying both French and Spanish are in Year 7. 50% of those Year 7 students are girls.

What percentage of all students are Year 7 girls studying both French and Spanish?

Worked Solution
Language students = 70% of all students

French students = 40% of 70%
= 28% of all students

French and Spanish students = 25% of 28%
= 7% of all students

Year 7 French and Spanish students = 20% of 7%
= 1.4% of all students

Year 7 girls studying French and Spanish = 50% of 1.4%
= 0.7%

∴\therefore 0.7% of all students are Year 7 girls studying both French and Spanish.

Question Type

Answer Box

Variables

Variable nameVariable value
question
70% of students at a school study a language. 40% of language students study French. 25% of French students also study Spanish. 20% of those studying both French and Spanish are in Year 7. 50% of those Year 7 students are girls. What percentage of all students are Year 7 girls studying both French and Spanish?
workedSolution
| | | | ----------------------------:| ---------------------------- | | Language students | \= 70% of all students |

| | | | ----------------------------:| ---------------------------- | | French students | \= 40% of 70% | | | \= 28% of all students |

| | | | ----------------------------------:| ---------------------------- | | French and Spanish students | \= 25% of 28% | | | \= 7% of all students |

| | | | -----------------------------------------:| ---------------------------- | | Year 7 French and Spanish students | \= 20% of 7% | | | \= 1.4% of all students |

| | | | -----------------------------------------------:| ---------------------------- | | Year 7 girls studying French and Spanish | \= 50% of 1.4% | | | \= {{{correctAnswer0}}}% |

$\therefore$ {{{correctAnswer0}}}% of all students are Year 7 girls studying both French and Spanish.
correctAnswer0
0.7
prefix0
suffix0
%

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer00.7

%

Tags

  • staging_suejones