Number_gap-2026_682

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

682

Question

Two numbers multiply together to give 24 and add to give 10.

What is the larger of the two numbers?

Worked Solution

Testing factor pairs of 24:
1 ×\times 24 = 24, 1 + 24 = 25
2 ×\times 12 = 24, 2 + 12 = 14
3 ×\times 8 = 24, 3 + 8 = 11
4 ×\times 6 = 24, 4 + 6 = 10 ✓

The two numbers are 4 and 6.

∴\therefore The larger number is 6

Question Type

Answer Box

Variables

Variable nameVariable value
question
Two numbers multiply together to give 24 and add to give 10. What is the larger of the two numbers?
workedSolution
Testing factor pairs of 24:
| | | - | | 1 $\times$ 24 = 24, 1 + 24 = 25 | | 2 $\times$ 12 = 24, 2 + 12 = 14 | | 3 $\times$ 8 = 24, 3 + 8 = 11 | | 4 $\times$ 6 = 24, 4 + 6 = 10 ✓ |

The two numbers are 4 and 6. $\therefore$ The larger number is {{{correctAnswer0}}}
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

683

Question

Two numbers multiply together to give −18 and add to give 3.

What is the larger of the two numbers?

Worked Solution

Testing factor pairs of 18 with opposite signs:
1 ×\times (−18) = −18, 1 + (−18) = −17
2 ×\times (−9) = −18, 2 + (−9) = −7
3 ×\times (−6) = −18, 3 + (−6) = −3
6 ×\times (−3) = −18, 6 + (−3) = 3 ✓

The two numbers are 6 and −3.

∴\therefore The larger number is 6

Question Type

Answer Box

Variables

Variable nameVariable value
question
Two numbers multiply together to give −18 and add to give 3. What is the larger of the two numbers?
workedSolution
Testing factor pairs of 18 with opposite signs:
| | | - | | 1 $\times$ (−18) = −18, 1 + (−18) = −17 | | 2 $\times$ (−9) = −18, 2 + (−9) = −7 | | 3 $\times$ (−6) = −18, 3 + (−6) = −3 | | 6 $\times$ (−3) = −18, 6 + (−3) = 3 ✓ |

The two numbers are 6 and −3. $\therefore$ The larger number is {{{correctAnswer0}}}
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

684

Question

Two numbers multiply together to give −20 and add to give −1.

What is the smaller of the two numbers?

Worked Solution

Testing factor pairs of 20 with opposite signs:
1 ×\times (−20) = −20, 1 + (−20) = −19
2 ×\times (−10) = −20, 2 + (−10) = −8
4 ×\times (−5) = −20, 4 + (−5) = −1 ✓

The two numbers are 4 and −5.

∴\therefore The smaller number is -5

Question Type

Answer Box

Variables

Variable nameVariable value
question
Two numbers multiply together to give −20 and add to give −1. What is the smaller of the two numbers?
workedSolution
Testing factor pairs of 20 with opposite signs:
| | | - | | 1 $\times$ (−20) = −20, 1 + (−20) = −19 | | 2 $\times$ (−10) = −20, 2 + (−10) = −8 | | 4 $\times$ (−5) = −20, 4 + (−5) = −1 ✓ |

The two numbers are 4 and −5. $\therefore$ The smaller number is {{{correctAnswer0}}}
correctAnswer0
-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
correctAnswer0-5

Variant 3

DifficultyLevel

685

Question

Two numbers multiply together to give 18 and add to give −9.

What is the larger of the two numbers?

Worked Solution

Both numbers must be negative since the product is positive and the sum is negative.

Testing negative factor pairs of 18:
(−1) ×\times (−18) = 18, (−1) + (−18) = −19
(−2) ×\times (−9) = 18, (−2) + (−9) = −11
(−3) ×\times (−6) = 18, (−3) + (−6) = −9 ✓

The two numbers are −3 and −6.

∴\therefore The larger number is -3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Two numbers multiply together to give 18 and add to give −9. What is the larger of the two numbers?
workedSolution
Both numbers must be negative since the product is positive and the sum is negative. Testing negative factor pairs of 18:
| | | - | | (−1) $\times$ (−18) = 18, (−1) + (−18) = −19 | | (−2) $\times$ (−9) = 18, (−2) + (−9) = −11 | | (−3) $\times$ (−6) = 18, (−3) + (−6) = −9 ✓ |

The two numbers are −3 and −6. $\therefore$ The larger number is {{{correctAnswer0}}}
correctAnswer0
-3
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
correctAnswer0-3

Variant 4

DifficultyLevel

684

Question

Two numbers multiply together to give 24 and add to give −11

What is the smaller of the two numbers?

Worked Solution

Both numbers must be negative since the product is positive and the sum is negative.

Testing negative factor pairs of 24:
(−1) ×\times (−24) = 24, (−1) + (−24) = −25
(−2) ×\times (−12) = 24, (−2) + (−12) = −14
(−3) ×\times (−8) = 24, (−3) + (−8) = −11 ✓

The two numbers are −3 and −8.

∴\therefore The smaller number is -8

Question Type

Answer Box

Variables

Variable nameVariable value
question
Two numbers multiply together to give 24 and add to give −11 What is the smaller of the two numbers?
workedSolution
Both numbers must be negative since the product is positive and the sum is negative. Testing negative factor pairs of 24:
| | | - | | (−1) $\times$ (−24) = 24, (−1) + (−24) = −25 | | (−2) $\times$ (−12) = 24, (−2) + (−12) = −14 | | (−3) $\times$ (−8) = 24, (−3) + (−8) = −11 ✓ |

The two numbers are −3 and −8. $\therefore$ The smaller number is {{{correctAnswer0}}}
correctAnswer0
-8
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
correctAnswer0-8

Tags

  • staging_suejones