Prep for the Mathematical Reasoning subject test with this GED math practice test (answers at the end of the post).

Need more practice? Check out these other question sets:

- GED Math Practice Questions
- GED Geometry Sample Problems
- GED Geometry Word Problems
- GED Data Analysis Questions
- GED Probability

## GED Math Practice Test

1. Which choice shows numbers in order from least to greatest?

A) .71, ^{7}⁄_{10}, 7 × 10^{-2}, 7 ^{99}⁄_{100}

B) 7 × 10^{-2}, 7 ^{99}⁄_{100}, ^{7}⁄_{10}, .71

C) .71, 7 × 10^{-2}, 7 ^{99}⁄_{100}, ^{7}⁄_{10}

D) 7 × 10^{-2}, 7⁄_{10}, .71, 7 ^{99}⁄_{100}

2. A start-up beverage company sold 32,138 bottles of cherry soda last year. Each bottle of soda was sold for $2.79. Which figure below is the best estimate for how much revenue the company earned from its cherry soda?

A) $69,000

B) $80,000

C) $90,000

D) $99,000

3. Which choice shows the correct factorization of the following expression?

15x^{2}-45x

A) 15x(x-3)

B) 15(x-3x)

C) 15x(x^{2}-3x)

D) 15(x^{2}-3)

4. Simplify the following expression.

(7-3)^{2}÷4+5-4×2

A) 1

B) 6

C) 8

D) 10

5. Find the value of x in the following equation.

2(x^{2}-5)=8

A) 1

B) 2

C) 3

D) 4

6. What is the value of x given the following system of equations?

y-2x=2

7x-5=2y

A) 8

B) 6

C) 4

D) 3

7. Solve the following inequality.

4x > 2(-15 + 1)

A) x < -7

B) x > -7

C) x < 7

D) x > 7

8. Which choice shows the sum of the following two polynomials?

(2x^{2}-4x+3)+ (-6x^{2}+7x-4)

A) -4x^{2}+3x-1

B) -8x^{2}-11x-7

C) 4x^{2}-3x+1

D) 8x^{2}+11x+7

9. Oliver pays $519.20 on a computer that is on sale. The computer is regularly priced at $649. What was the percent discount Oliver received on the computer?

A) 15%

B) 20%

C) 25%

D) 30%

**Use the following table to answer questions 10-12. **

Jack keeps track of the number of birds who visit his backyard feeder each week. Last week he recorded the following species and their number of visits.

## Bird Visits the Week of March 13

Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday | |
---|---|---|---|---|---|---|---|

juncos | 23 | 21 | 17 | 20 | 12 | 18 | 22 |

sparrows | 35 | 42 | 43 | 48 | 31 | 37 | 46 |

finches | 12 | 13 | 11 | 16 | 9 | 11 | 18 |

cardinals | 4 | 2 | 1 | 1 | 0 | 1 | 2 |

woodpeckers | 2 | 0 | 1 | 2 | 0 | 0 | 1 |

starlings | 7 | 2 | 5 | 8 | 3 | 5 | 7 |

10. What fraction of the birds who visited the feeder on Tuesday were sparrows?

A) ^{21}⁄_{40}

B) ^{1}⁄_{6}

C) ^{21}⁄_{19}

D) ^{1}⁄_{5}

11. What fraction of the birds who visited Jack’s feeder last Saturday and Sunday were juncos?

A) ^{70}⁄_{111}

B) ^{5}⁄_{16}

C) ^{5}⁄_{21}

D) ^{9}⁄_{11}

12. What was the ratio of finches to cardinals that visited Jack’s feeder last week?

A) 90:101

B) 11:90

C) 11:101

D) 90:11

13. Clara goes trick-or-treating and gets 24 pieces of chocolate, 12 pieces of gum, 5 pieces of licorice, and 18 suckers. If she randomly pulls a piece of candy from her trick-or-treat bag, what is the probability of her pulling out a piece of gum?

A) 12 out of 47

B) 1 out of 4

C) 12 out of 59

D) 1 out of 12

14. Luna and Alex are choosing a menu for their reception. They have 4 choices of appetizers, 6 choices of entrees, 5 choices of side dishes, and 3 choices of cake. How many different menu combinations are possible?

A) 6

B) 18

C) 150

D) 360

15. The area of a circle is 81π cm. What is the length of its radius?

A) 3 centimeters

B) 9 centimeters

C) 18 centimeters

D) 81 centimeters

16. Theodore needs to cover a bulletin board with paper. The bulletin board is 6 feet by 4 feet. He has 8 square feet of paper. How many more square feet of paper does he need to cover the bulletin board?

A) 24 square feet

B) 20 square feet

C) 16 square feet

D) 12 square feet

17. A triangle has a base measuring 15 centimeters and a height measuring 13 centimeters. How long is its hypotenuse?

A) 195 centimeters

B) √394 centimeters

C) √28 centimeters

D) 784 centimeters

18. A swimming pool holds 2,450 cubic feet of water. The swimming pool is 35 feet long and 14 feet wide. How deep is the swimming pool?

A) 4 feet

B) 5 feet

C) 6 feet

D) 7 feet

**Use the following table to answer questions 19-21.**

An ice cream shop surveyed 10 customers, asking them to rate chocolate flavors on a scale of 1 to 10, with 10 being the best possible taste.

## Customers' Chocolate Flavor Preference

Fudge Swirl Rating | Brownie Chunk Rating | Classic Rating | |
---|---|---|---|

Customer 1 | 10 | 7 | 9 |

Customer 2 | 6 | 7 | 10 |

Customer 3 | 10 | 9 | 8 |

Customer 4 | 7 | 8 | 9 |

Customer 5 | 9 | 8 | 10 |

Customer 6 | 7 | 10 | 8 |

Customer 7 | 8 | 6 | 5 |

Customer 8 | 6 | 7 | 8 |

Customer 9 | 10 | 9 | 7 |

Customer 10 | 9 | 7 | 6 |

19. Rank the flavors from the flavor with the highest mean rating to the flavor with the lowest mean rating.

A) Fudge Swirl, Classic, Brownie Chunk

B) Classic, Brownie Chunk, Fudge Swirl

C) Brownie Chunk, Fudge Swirl, Classic

D) Fudge Swirl, Brownie Chunk, Classic

20. What was the median rating for Fudge Swirl?

A) 10

B) 9

C) 8.5

D) 7.5

21. What was the mode of the ratings for Classic?

A) 7

B) 8

C) 9

D) 10

22. What is the slope-intercept form of a line having a slope of ^{1}⁄_{2} and a y-intercept of 4?

A) 4= ^{1}⁄_{2}x+b

B) ^{1}⁄_{2}=4y+x

C) x=4y+^{1}⁄_{2}

D) y=^{1}⁄_{2}x+4

23. Solve the following inequality.

-4y+8>-12

A) y<5

B) y>5

C) y<1

D) y>1

24. Find the difference of the following two polynomials:

(2x^{2}-4x+5)-(-6x^{2}-7x+4)

A) -4x^{2}+3x+1

B) 4x^{2}+11x-9

C) 8x^{2}+3x+1

D) -8x^{2}+11x-9

25. Amelia has spends $462 on groceries in the month of February. She spent $205 on fresh produce. About what percentage of her grocery money went to fresh produce?

A) 2.25%

B) 44%

C) 56%

D) 80%

### Answer Key

**1. D**

7 ×10^{-2}=^{7}⁄_{100}

^{7}⁄_{10}=^{70}⁄_{100}

.71=^{71}⁄_{100}

7 ^{99}⁄_{100}=^{799}⁄_{100}

**2. C**

32,138 rounds down to 30,000; $2.79 rounds up to 3. 30,000 ×3=90,000. The exact amount is $89,665.02, so $90,000 is the closest estimate among the answer choices.

**3. A**

The terms in the expression have a greatest common factor of 15x.

**4. A**

(7-3)^{2}÷4+5-4×2

4^{2}÷4+5-4×2

16÷4+5-4×2

4+5-8

9-8=1

**5. C**

2(x^{2}-5)=8

x^{2}-5=4

x^{2}=9

x=3

**6. D**

Isolate the y in the first equation:

y-2x=2

y=2+2x

Substitute the expression of y into the second equation and solve for x:

7x-5=2y

7x-5=2(2+2x)

7x-5=4+4x

7x=9+4x

3x=9

x=3

**7. B**

4x>2(-15+1)

4x>2(-14)

4x>-28

x>-7

**8. A**

(2x^{2}-4x+3)+ (-6x^{2}+7x-4)

2x^{2}-6x^{2}-4x+7x+3-4

-4x^{2}-4x+7x+3-4

-4x^{2}+3x+3-4

-4x^{2}+3x-1

**9. B**

Find the discount.

649-519.20=129.80

Find what percent of the total price the discount is.

129.80÷649=.2=20%

**10. A**

42 sparrows that visited on Tuesday. Find the number of sparrows to the number of all birds who visited, including sparrows:

21+42+13+2+2 = 80

^{42}⁄_{80}=^{21}⁄_{40}

**11. C**

Find the number of juncos that visited on Saturday and Sunday.

18+22=40

Find the number of juncos on both days to the number of all birds who visited on both days, including juncos:

18+22+37+46+11+18+1+2+1+5+7=168

^{40}⁄_{168}=^{5}⁄_{21}

**12. D**

90 finches visited the feeder last week, and 11 cardinals visited the feeder last week. The ratio is 90 finches per every 11 cardinals: 90:11.

**13. C**

The bag contains 12 pieces of gum. There are 59 possible pieces of candy she could randomly pull from the bag. 12 out of 59 times, she will pull out a piece of gum.

**14. D**

Use the fundamental counting principle to multiply the number of choices together:

4(6)(5)(3)=360

**15. B**

Use the formula for the area of a circle:

A=πr^{2}

81π=πr^{2}

81=r^{2}

9=r

**16. C**

Find the area of the bulletin board:

A=lw

A=6(4)

A=24

Subtract the paper Theodore already has:

24-8=16

**17. B**

Use the Pythagorean Theorem to solve:

a^{2}+b^{2}=c^{2}

15^{2}+13^{2}=c^{2}

225+169=c^{2}

394=c^{2}

√394=c

**18. B**

Use the formula for the volume of a rectangular prism:

V=lwh

2,450=35(14)h

2,450=490h

5=h

**19. A**

Mean rating for Fudge Swirl:

10+6+10+7+9+7+8+6+10+10=82

82÷10=8.2

Mean rating for Classic:

9+10+8+9+10+8+5+8+7+6=80

80÷10=8

Mean rating for Brownie Chunk:

7+7+9+8+8+10+6+7+9+7=78

78÷10=7.8

**20. C**

The median is the middle term:

6,6,7,7,8,9,9,10,10,10

8+9=17

17÷2=8.5

**21. B**

The mode is the number that appears most frequently:

5,6,7,**8,8,8**,9,9,10,10

**22. D**

The formula for slope-intercept form is y=mx+b, where m is the slope, and b is the y-intercept.

**23. A**

You must flip the sign when dividing or multiplying by a negative number.

-4y+8>-12

-4y>-20

y<5

**24. C**

Change the signs of the polynomial being subtracted, then add:

2x^{2}-4x+5+6x^{2}+7x-4

2x^{2}+6x^{2}-4x+7x+5-4

8x^{2}+3x+1

**25. B**

205÷462=0.4437=44%

Number 4 is completely incorrect. The work in the answer key is incorrect as well. Not going to use the rest of this test.

Hi Lydia,

Sorry it took so long to respond, but this is not incorrect. You can verify this using a powerful tool like Wolfram Alpha. According to the order of operations, we would first solve the parentheses:

(7-3)^2 ÷ 4 + 5 – 4 × 2

(4)^2 ÷ 4 + 5 – 4 × 2

Next, the exponent:

(4)^2 ÷ 4 + 5 – 4 × 2

16 ÷ 4 + 5 – 4 × 2

Then division and multiplication, in left-to-right order:

16 ÷ 4 + 5 – 4 × 2

4 + 5 – 4 × 2

4 + 5 – 8

Then, finally, addition and subtraction, also left-to-right:

4 + 5 – 8

9 – 8

1

I hope this clarifies for you and anyone else! 🙂

I don’t understand how number 7 is solved. Where does the 2 come from? :”(

Hi Yohai,

Thanks for pointing this out! It looks like there are a few issues with number 7–two of the answer choices are missing as well! It appears that the original problem should have also included the 2. I’m going to send this along to our blog team so that we can find the original question and correct this mistake. We always appreciate it when students let us know about issues like these 🙂