50150

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

527

Question

At the start of school, every child chooses one sport.

The table shows how many children chose each sport.


Rugby Swimming AFL Tennis
Girls 40 35 15 30
Boys 20 55 25 10


Select the statement that is true.

Worked Solution

By trial and error, consider option 3:

Total girls = 40 + 35 + 15 + 30 = 120
14×120\dfrac{1}{4} \times 120 = 30

∴\therefore One quarter of the girls chose tennis.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
At the start of school, every child chooses one sport. The table shows how many children chose each sport.
>>| | Rugby | Swimming |AFL| Tennis| |:-:|:-:|:-:|:-:|:-:| | Girls | 40| 35|15|30| | Boys| 20| 55|25|10|

Select the statement that is true.
workedSolution
By trial and error, consider option 3: Total girls = 40 + 35 + 15 + 30 = 120
| | | | --------------------: | -------------- | | $\dfrac{1}{4} \times 120$ | = 30 |

$\therefore$ {{{correctAnswer}}}
correctAnswer
One quarter of the girls chose tennis.

Answers

Is Correct?Answer
x

In total, 100 children chose swimming.

x

Less than half the boys chose swimming.

✓

One quarter of the girls chose tennis.

x

The same number of boys and girls are at the school.

Variant 1

DifficultyLevel

529

Question

At the start of the cricket season, every player chooses one specialty to practice.

The table shows how many players chose each specialty.


Bowling Out Field Slips Batting
Females 10 12 17 21
Males 22 8 15 25


Select the statement that is true.

Worked Solution

By trial and error, consider option 2:

Total females = 10 + 12 + 17 + 21 = 60

Half females = 30

Females bowling or batting = 10 + 21 = 31

∴\therefore More than half the females chose either bowling or batting.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
At the start of the cricket season, every player chooses one specialty to practice. The table shows how many players chose each specialty.
>>| | Bowling | Out Field |Slips| Batting| |:-:|:-:|:-:|:-:|:-:| | Females | 10| 12|17|21| | Males| 22| 8|15|25|

Select the statement that is true.
workedSolution
By trial and error, consider option 2: Total females = 10 + 12 + 17 + 21 = 60 Half females = 30 Females bowling or batting = 10 + 21 = 31 $\therefore$ {{{correctAnswer}}}
correctAnswer
More than half the females chose either bowling or batting.

Answers

Is Correct?Answer
x

There are more females playing than males.

✓

More than half the females chose either bowling or batting.

x

Half the males chose either slips or batting.

x

The same number of males and females are playing cricket.

Variant 2

DifficultyLevel

531

Question

At the school canteen, every child chooses one lunch option.

The table shows how many children chose each lunch.


Salad Bowl Sandwich Wrap Fruit Salad Bowl
Girls 15 21 10 14
Boys 12 25 15 20


Select the statement that is true.

Worked Solution

By trial and error, consider option 4:

Total boys = 12 + 25 + 15 + 20 = 72
16×72\dfrac{1}{6} \times 72 = 12

∴\therefore One sixth of the boys chose the salad bowl.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
At the school canteen, every child chooses one lunch option. The table shows how many children chose each lunch.
>>| | Salad Bowl | Sandwich |Wrap| Fruit Salad Bowl| |:-:|:-:|:-:|:-:|:-:| | Girls | 15| 21|10|14| | Boys| 12| 25|15|20|

Select the statement that is true.
workedSolution
By trial and error, consider option 4: Total boys = 12 + 25 + 15 + 20 = 72
| | | | --------------------: | -------------- | | $\dfrac{1}{6} \times 72$ | = 12 |

$\therefore$ {{{correctAnswer}}}
correctAnswer
One sixth of the boys chose the salad bowl.

Answers

Is Correct?Answer
x

The same number of boys and girls ordered lunch from the canteen.

x

One quarter of the girls and a quarter of the boys chose the salad bowl.

x

One third of the boys chose the wrap.

✓

One sixth of the boys chose the salad bowl.

Variant 3

DifficultyLevel

533

Question

At the start of Year 8, every child chooses one language.

The table shows how many children chose each language.


Spanish German French Japanese
Girls 21 16 23 24
Boys 22 21 16 21


Select the statement that is true.

Worked Solution

By trial and error, consider option 1:

Total girls = 21 + 16 + 23 + 24 = 84

14 ×\dfrac{1}{4}\ \times girls = 21 ⇒\Rightarrow 34=3×21=63\dfrac{3}{4} = 3 \times 21 = 63

German + French + Japanese = 16 + 23 + 24 = 63

∴\therefore Three quarters of the girls study either German, French or Japanese.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
At the start of Year 8, every child chooses one language. The table shows how many children chose each language.
>>| | Spanish| German |French| Japanese| |:-:|:-:|:-:|:-:|:-:| | Girls | 21| 16|23|24| | Boys| 22| 21|16|21|

Select the statement that is true.
workedSolution
By trial and error, consider option 1: Total girls = 21 + 16 + 23 + 24 = 84 $\dfrac{1}{4}\ \times$ girls = 21 $\Rightarrow$ $\dfrac{3}{4} = 3 \times 21 = 63$ German + French + Japanese = 16 + 23 + 24 = 63 $\therefore$ {{{correctAnswer}}}
correctAnswer
Three quarters of the girls study either German, French or Japanese.

Answers

Is Correct?Answer
✓

Three quarters of the girls study either German, French or Japanese.

x

Less than half the boys study Spanish or German.

x

The same fraction of boys study French as the girls studying Japanese

x

The same number of boys and girls were in Year 8.

Variant 4

DifficultyLevel

525

Question

At a children's party, each child can choose one pizza flavour.

The table shows how many children chose each type of pizza.


Cheese Margarita Pepperoni Hawaiian
Girls 9 6 5 4
Boys 8 4 10 2


Select the statement that is true.

Worked Solution

By trial and error, consider option 2:
Total girls = 9 + 6 + 5 + 4 = 24
Total boys = 8 + 4 + 10 + 2 = 24

∴\therefore The same number of girls and boys attended the party.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
At a children's party, each child can choose one pizza flavour. The table shows how many children chose each type of pizza.
>>| | Cheese| Margarita |Pepperoni| Hawaiian| |:-:|:-:|:-:|:-:|:-:| | Girls | 9| 6|5|4| | Boys| 8| 4|10|2|

Select the statement that is true.
workedSolution
By trial and error, consider option 2:
| | | | | --------------------: | -------------- | -------------- | | Total girls| = 9 + 6 + 5 + 4 | = 24 | | Total boys| = 8 + 4 + 10 + 2| = 24 |

$\therefore$ {{{correctAnswer}}}
correctAnswer
The same number of girls and boys attended the party.

Answers

Is Correct?Answer
x

More boys chose Cheese or Margarita than girls.

✓

The same number of girls and boys attended the party.

x

Half the number of girls chose either Margarita or Pepperoni.

x

One quarter of the boys chose Cheese.

Variant 5

DifficultyLevel

537

Question

At the start of athletics training, every child chooses one field event.

The table shows how many children chose each field event.


Shotput Discus Long Jump High Jump
8 Year Olds 12 16 10 18
9 Year Olds 15 14 24 17


Select the statement that is true.

Worked Solution

By trial and error, consider option 3:

Total 8 Year olds = 12 + 16 + 10 + 18 = 56

8 Year olds choosing discus = 1656\dfrac{16}{56} = 27\dfrac{2}{7}

Total 9 Year olds = 15 + 14 + 24 + 17 = 70

9 Year olds choosing discus = 1470\dfrac{14}{70} = 15\dfrac{1}{5}

Since 15\dfrac{1}{5} < 27\dfrac{2}{7},

∴\therefore A smaller fraction of total 9 year olds chose discus versus the same fraction of total 8 year olds that chose it.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
At the start of athletics training, every child chooses one field event. The table shows how many children chose each field event.
>>| | Shotput| Discus |Long Jump| High Jump| |:-:|:-:|:-:|:-:|:-:| | 8 Year Olds | 12| 16|10|18| | 9 Year Olds| 15| 14|24|17|

Select the statement that is true.
workedSolution
By trial and error, consider option 3: Total 8 Year olds = 12 + 16 + 10 + 18 = 56 8 Year olds choosing discus = $\dfrac{16}{56}$ = $\dfrac{2}{7}$ Total 9 Year olds = 15 + 14 + 24 + 17 = 70 9 Year olds choosing discus = $\dfrac{14}{70}$ = $\dfrac{1}{5}$ Since $\dfrac{1}{5}$ < $\dfrac{2}{7}$, $\therefore$ {{{correctAnswer}}}
correctAnswer
A smaller fraction of total 9 year olds chose discus versus the same fraction of total 8 year olds that chose it.

Answers

Is Correct?Answer
x

More than half the 9 year olds chose shotput or high jump.

x

Less than one quarter of the 8 year olds chose discus.

✓

A smaller fraction of total 9 year olds chose discus versus the same fraction of total 8 year olds that chose it.

x

The same number of 8 year olds and 9 year olds were choosing field events.

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