Algebra, NAPX-H3-CA20

Question

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Worked Solution

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Variant 0

DifficultyLevel

554

Question

An unknown number is added to −3.

The result is multiplied by 2 to give an answer of 6.

Which of these is the unknown number?

Worked Solution

Strategy 1

Trial each option:

If unknown number = 6

6 −- 3 = 3


2 ×\times 3 = 6 (correct)


Strategy 2 (advanced)

Let n\large n = unknown number

Working backwards:

3 ×\times 2 = 6


⇒ n\Rightarrow\ \large n + (−- 3) = 3


∴ n\therefore\ \large n = 6

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
An unknown number is added to −3. The result is multiplied by 2 to give an answer of 6. Which of these is the unknown number?
workedSolution
Strategy 1 Trial each option: If unknown number = 6 >6 $-$ 3 = 3
>2 $\times$ 3 = 6 (correct)
Strategy 2 (advanced) Let $\large n$ = unknown number Working backwards: >3 $\times$ 2 = 6
>$\Rightarrow\ \large n$ + ($-$ 3) = 3
$\therefore\ \large n$ = {{{correctAnswer}}}
correctAnswer
6

Answers

Is Correct?Answer
x

−- 3

x

−- 1

✓

6

x

15

Variant 1

DifficultyLevel

552

Question

An unknown number is added to −5.

The result is multiplied by 3 to give an answer of 9.

Which of these is the unknown number?

Worked Solution

Solution 1

Trial each option:

If unknown number = 8

8 −- 5 = 3

3 ×\times 3 = 9 (correct)


Solution 2 (advanced)

Let n\large n = unknown number

Working backwards:

3 ×\times 3 = 9

⇒ n\Rightarrow\ \large n + (−- 5) = 3

∴ n\therefore\ \large n = 8

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
An unknown number is added to −5. The result is multiplied by 3 to give an answer of 9. Which of these is the unknown number?
workedSolution
Solution 1 Trial each option: If unknown number = 8 8 $-$ 5 = 3 3 $\times$ 3 = 9 (correct)
Solution 2 (advanced) Let $\large n$ = unknown number Working backwards: 3 $\times$ 3 = 9 $\Rightarrow\ \large n$ + ($-$ 5) = 3 $\therefore\ \large n$ = {{{correctAnswer}}}
correctAnswer
8

Answers

Is Correct?Answer
x

−- 6

x

−- 2

x

4

✓

8

Variant 2

DifficultyLevel

560

Question

An unknown number is added to 2.

The result is multiplied by 4 to give an answer of −- 4.

Which of these is the unknown number?

Worked Solution

Solution 1

Trial each option:

If unknown number = −- 3

−- 3 + 2 = −- 1

4 ×\times −- 1 = −- 4 (correct)


Solution 2 (advanced)

Let n\large n = unknown number

Working backwards:

4 ×\times −- 1 = −- 4

⇒ n\Rightarrow\ \large n + 2 = −- 1

∴ n\therefore\ \large n = −- 3

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
An unknown number is added to 2. The result is multiplied by 4 to give an answer of $-$ 4. Which of these is the unknown number?
workedSolution
Solution 1 Trial each option: If unknown number = $-$ 3 $-$ 3 + 2 = $-$ 1 4 $\times$ $-$ 1 = $-$ 4 (correct)
Solution 2 (advanced) Let $\large n$ = unknown number Working backwards: 4 $\times$ $-$ 1 = $-$ 4 $\Rightarrow\ \large n$ + 2 = $-$ 1 $\therefore\ \large n$ = {{{correctAnswer}}}
correctAnswer
$-$ 3

Answers

Is Correct?Answer
✓

−- 3

x

−- 1

x

1

x

2

Variant 3

DifficultyLevel

556

Question

An unknown number is added to 5.

The result is multiplied by 3 to give an answer of −- 6.

Which of these is the unknown number?

Worked Solution

Solution 1

Trial each option:

If unknown number = −- 7

−- 7 + 5 = −- 2

3 ×\times −- 2 = −- 6 (correct)


Solution 2 (advanced)

Let n\large n = unknown number

Working backwards:

3 ×\times −- 2 = −- 6

⇒ n\Rightarrow\ \large n + 5 = −- 2

∴ n\therefore\ \large n = −- 7

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
An unknown number is added to 5. The result is multiplied by 3 to give an answer of $-$ 6. Which of these is the unknown number?
workedSolution
Solution 1 Trial each option: If unknown number = $-$ 7 $-$ 7 + 5 = $-$ 2 3 $\times$ $-$ 2 = $-$ 6 (correct)
Solution 2 (advanced) Let $\large n$ = unknown number Working backwards: 3 $\times$ $-$ 2 = $-$ 6 $\Rightarrow\ \large n$ + 5 = $-$ 2 $\therefore\ \large n$ = {{{correctAnswer}}}
correctAnswer
$-$ 7

Answers

Is Correct?Answer
✓

−- 7

x

−- 4

x

3

x

4

Variant 4

DifficultyLevel

548

Question

An unknown number is added to −1.

The result is multiplied by 2 to give an answer of −8.

Which of these is the unknown number?

Worked Solution

Solution 1

Trial each option:

If unknown number = −- 3

−- 3 + (−- 1) = −- 4

2 ×\times −- 4 = −- 8 (correct)


Solution 2 (advanced)

Let n\large n = unknown number

Working backwards:

2 ×\times −- 4 = −- 8

⇒ n\Rightarrow\ \large n + (−- 1) = −- 4

∴ n\therefore\ \large n = −- 3

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
An unknown number is added to −1. The result is multiplied by 2 to give an answer of −8. Which of these is the unknown number?
workedSolution
Solution 1 Trial each option: If unknown number = $-$ 3 $-$ 3 + ($-$ 1) = $-$ 4 2 $\times$ $-$ 4 = $-$ 8 (correct)
Solution 2 (advanced) Let $\large n$ = unknown number Working backwards: 2 $\times$ $-$ 4 = $-$ 8 $\Rightarrow\ \large n$ + ($-$ 1) = $-$ 4 $\therefore\ \large n$ = {{{correctAnswer}}}
correctAnswer
$-$ 3

Answers

Is Correct?Answer
x

−- 5

✓

−- 3

x

1

x

4

Variant 5

DifficultyLevel

562

Question

An unknown number is added to −2.

The result is multiplied by 4 to give an answer of −- 6.

Which of these is the unknown number?

Worked Solution

Solution 1

Trial each option:

If unknown number = 12\dfrac{1}{2}

−- 2 + 12\dfrac{1}{2} = −- 1121\dfrac{1}{2}

4 ×\times −- 1121\dfrac{1}{2} = −- 6 (correct)


Solution 2 (advanced)

Let n\large n = unknown number

Working backwards:

4 ×\times −- 1121\dfrac{1}{2} = −- 86

⇒ n\Rightarrow\ \large n + (−- 2) = −- 1121\dfrac{1}{2}

∴ n\therefore\ \large n = 12\dfrac{1}{2}

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
An unknown number is added to −2. The result is multiplied by 4 to give an answer of $-$ 6. Which of these is the unknown number?
workedSolution
Solution 1 Trial each option: If unknown number = $\dfrac{1}{2}$ $-$ 2 + $\dfrac{1}{2}$ = $-$ $1\dfrac{1}{2}$ 4 $\times$ $-$ $1\dfrac{1}{2}$ = $-$ 6 (correct)
Solution 2 (advanced) Let $\large n$ = unknown number Working backwards: 4 $\times$ $-$ $1\dfrac{1}{2}$ = $-$ 86 $\Rightarrow\ \large n$ + ($-$ 2) = $-$ $1\dfrac{1}{2}$ $\therefore\ \large n$ = {{{correctAnswer}}}
correctAnswer
$\dfrac{1}{2}$

Answers

Is Correct?Answer
x

−- 1121\dfrac{1}{2}

✓

12\dfrac{1}{2}

x

2

x

3123\dfrac{1}{2}

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