Number, NAPX-H4-CA27

Question

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Worked Solution

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Variant 0

DifficultyLevel

709

Question

A loaf of bread is on sale with a 15% discount.

In the last hour of trading, the bread is reduced a further 20% on the already discounted price.

What is the overall percentage discount on the bread?

Worked Solution

Strategy 1

Assume the bread costs $1.00 (say)

Cost after 15% discount = $0.85

Cost after further 20% discount
= 0.85 − (20% × 0.85)
= 0.85 − 0.17
= $0.68

∴\therefore Overall discount = (1 − 0.68) × 100
= 32%

Strategy 2 (advanced)
Overall discount = 1 − (0.85 × 0.80)
= 1 − 0.68
= 0.32
= 32%

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A loaf of bread is on sale with a 15% discount. In the last hour of trading, the bread is reduced a further 20% on the already discounted price. What is the overall percentage discount on the bread?
workedSolution
Strategy 1 Assume the bread costs $1.00 (say) Cost after 15% discount = $0.85 sm_nogap Cost after further 20% discount
>>|| |-| |= 0.85 − (20% × 0.85)| |= 0.85 − 0.17| |= $0.68|

| | | | --------------------- | -------------- | | $\therefore$ Overall discount | \= (1 − 0.68) × 100 | | | \= {{{correctAnswer}}} |

sm_nogap Strategy 2 (advanced)
| | | | --------------------- | -------------- | | Overall discount | \= 1 − (0.85 × 0.80) | | | \= 1 − 0.68 | || \= 0.32| || \= {{{correctAnswer}}}|
correctAnswer
32%

Answers

Is Correct?Answer
x

1.5%

x

7.25%

x

27.5%

✓

32%

x

35%

Variant 1

DifficultyLevel

711

Question

A container of salad is on sale with a 10% discount.

One hour before the supermarket closes, the salad is reduced a further 20% on the already discounted price.

What is the overall percentage discount on the salad?

Worked Solution

Strategy 1

Assume the salad costs $1.00 (say)

Cost after 10% discount = $0.90

Cost after further 20% discount
= 0.90 − (20% × 0.90)
= 0.90 − 0.18
= $0.72

∴\therefore Overall discount = (1 − 0.72) × 100
= 28%

Strategy 2 (advanced)
Overall discount = 1 − (0.90 × 0.80)
= 1 − 0.72
= 0.28
= 28%

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A container of salad is on sale with a 10% discount. One hour before the supermarket closes, the salad is reduced a further 20% on the already discounted price. What is the overall percentage discount on the salad?
workedSolution
Strategy 1 Assume the salad costs $1.00 (say) Cost after 10% discount = $0.90 sm_nogap Cost after further 20% discount
>>|| |-| |= 0.90 − (20% × 0.90)| |= 0.90 − 0.18| |= $0.72|

| | | | --------------------- | -------------- | | $\therefore$ Overall discount | \= (1 − 0.72) × 100 | | | \= {{{correctAnswer}}} |

sm_nogap Strategy 2 (advanced)
| | | | --------------------- | -------------- | | Overall discount | \= 1 − (0.90 × 0.80) | | | \= 1 − 0.72 | || \= 0.28| || \= {{{correctAnswer}}}|
correctAnswer
28%

Answers

Is Correct?Answer
x

2.5%

x

17%

✓

28%

x

35%

x

72%

Variant 2

DifficultyLevel

712

Question

A car is offered for sale with a 15% discount.

In the end of financial year sale, the car is reduced a further 10% on the already discounted price.

What is the overall percentage discount on the car?

Worked Solution

Strategy 1

Assume the car costs $1.00 (say)

Cost after 15% discount = $0.85

Cost after further 10% discount
= 0.85 − (10% × 0.85)
= 0.85 − 0.085
= $0.765

∴\therefore Overall discount = (1 − 0.765) × 100
= 23.5%

Strategy 2 (advanced)
Overall discount = 1 − (0.85 × 0.90)
= 1 − 0.765
= 0.235
= 23.5%

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A car is offered for sale with a 15% discount. In the end of financial year sale, the car is reduced a further 10% on the already discounted price. What is the overall percentage discount on the car?
workedSolution
Strategy 1 Assume the car costs $1.00 (say) Cost after 15% discount = $0.85 sm_nogap Cost after further 10% discount
>>|| |-| |= 0.85 − (10% × 0.85)| |= 0.85 − 0.085| |= $0.765|

| | | | --------------------- | -------------- | | $\therefore$ Overall discount | \= (1 − 0.765) × 100 | | | \= {{{correctAnswer}}} |

sm_nogap Strategy 2 (advanced)
| | | | --------------------- | -------------- | | Overall discount | \= 1 − (0.85 × 0.90) | | | \= 1 − 0.765 | || \= 0.235| || \= {{{correctAnswer}}}|
correctAnswer
23.5%

Answers

Is Correct?Answer
x

5%

✓

23.5%

x

25%

x

50%

x

76.5%

Variant 3

DifficultyLevel

713

Question

A punnet of blueberries is on sale with a 20% discount.

In the last hour of trading, the blueberries are reduced a further 20% on the already discounted price.

What is the overall percentage discount on the blueberries?

Worked Solution

Strategy 1

Assume the blueberries cost $1.00 (say)

Cost after 20% discount = $0.80

Cost after further 20% discount
= 0.80 − (20% × 0.80)
= 0.80 − 0.16
= $0.64

∴\therefore Overall discount = (1 − 0.64) × 100
= 36%

Strategy 2 (advanced)
Overall discount = 1 − (0.80 × 0.80)
= 1 − 0.64
= 0.36
= 36%

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A punnet of blueberries is on sale with a 20% discount. In the last hour of trading, the blueberries are reduced a further 20% on the already discounted price. What is the overall percentage discount on the blueberries?
workedSolution
Strategy 1 Assume the blueberries cost $1.00 (say) Cost after 20% discount = $0.80 sm_nogap Cost after further 20% discount
>>|| |-| |= 0.80 − (20% × 0.80)| |= 0.80 − 0.16| |= $0.64|

| | | | --------------------- | -------------- | | $\therefore$ Overall discount | \= (1 − 0.64) × 100 | | | \= {{{correctAnswer}}} |

sm_nogap Strategy 2 (advanced)
| | | | --------------------- | -------------- | | Overall discount | \= 1 − (0.80 × 0.80) | | | \= 1 − 0.64 | || \= 0.36| || \= {{{correctAnswer}}}|
correctAnswer
36%

Answers

Is Correct?Answer
x

20%

✓

36%

x

40%

x

60%

x

64%

Variant 4

DifficultyLevel

714

Question

A gas heater is on sale with a 15% discount.

At the end of winter, the heater is reduced a further 25% on the already discounted price.

What is the overall percentage discount on the heater?

Worked Solution

Strategy 1

Assume the heater costs $1.00 (say)

Cost after 15% discount = $0.85

Cost after further 25% discount
= 0.85 − (25% × 0.85)
= 0.85 − 0.2125
= $0.6375

∴\therefore Overall discount = (1 − 0.6375) × 100
= 36.25%

Strategy 2 (advanced)
Overall discount = 1 − (0.85 × 0.75)
= 1 − 0.6375
= 0.3625
= 36.25%

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A gas heater is on sale with a 15% discount. At the end of winter, the heater is reduced a further 25% on the already discounted price. What is the overall percentage discount on the heater?
workedSolution
Strategy 1 Assume the heater costs $1.00 (say) Cost after 15% discount = $0.85 sm_nogap Cost after further 25% discount
>>|| |-| |= 0.85 − (25% × 0.85)| |= 0.85 − 0.2125| |= $0.6375|

| | | | --------------------- | -------------- | | $\therefore$ Overall discount | \= (1 − 0.6375) × 100 | | | \= {{{correctAnswer}}} |

sm_nogap Strategy 2 (advanced)
| | | | --------------------- | -------------- | | Overall discount | \= 1 − (0.85 × 0.75) | | | \= 1 − 0.6375 | || \= 0.3625| || \= {{{correctAnswer}}}|
correctAnswer
36.25%

Answers

Is Correct?Answer
x

63.75%

x

60%

x

85

x

40

✓

36.25%

Variant 5

DifficultyLevel

722

Question

A fan is on sale with a 12% discount.

At the end of summer, the fan is reduced a further 16% on the already discounted price.

What is the overall percentage discount on the heater?

Worked Solution

Strategy 1

Assume the fan costs $1.00 (say)

Cost after 12% discount = $0.88

Cost after further 16% discount
= 0.88 − (16% × 0.88)
= 0.88 − 0.1408
= $0.7392

∴\therefore Overall discount = (1 − 0.7392) × 100
= 26.08%

Strategy 2 (advanced)
Overall discount = 1 − (0.88 × 0.84)
= 1 − 0.7392
= 0.2608
= 26.08%

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A fan is on sale with a 12% discount. At the end of summer, the fan is reduced a further 16% on the already discounted price. What is the overall percentage discount on the heater?
workedSolution
Strategy 1 Assume the fan costs $1.00 (say) Cost after 12% discount = $0.88 sm_nogap Cost after further 16% discount
>>|| |-| |= 0.88 − (16% × 0.88)| |= 0.88 − 0.1408| |= $0.7392|

| | | | --------------------- | -------------- | | $\therefore$ Overall discount | \= (1 − 0.7392) × 100 | | | \= {{{correctAnswer}}} |

sm_nogap Strategy 2 (advanced)
| | | | --------------------- | -------------- | | Overall discount | \= 1 − (0.88 × 0.84) | | | \= 1 − 0.7392 | || \= 0.2608| || \= {{{correctAnswer}}}|
correctAnswer
26.08%

Answers

Is Correct?Answer
x

73.92%

x

72%

x

26%

✓

26.08%

x

19.2%

Tags

  • ms_ca