GED Mathematical Reasoning Practice Test

25 practice questions

Choose an answer, then check it under Show answer.

1. Question 1 of 25Easy

   What is the value of y in the equation (1/2)y + 3/4 = 7/4?

   1. AA. 5
   2. BB. 1
   3. CC. 1/2
   4. DD. 2
   Show answer to question 1

   Answer: D. 2

   Subtracting 3/4 from both sides leaves (1/2)y = 1, and multiplying both sides by 2 gives y = 2. A common error is forgetting to multiply by the reciprocal in the final step, which leads to the incorrect result of 1.

2. Question 2 of 25Medium

   A tablet has an original price of $240. The store offers a 20% discount on the original price. At checkout, a shopper uses a coupon for an additional 10% off the discounted price. What is the final price of the tablet before tax?

   1. AA. $168.00
   2. BB. $192.00
   3. CC. $216.00
   4. DD. $172.80
   Show answer to question 2

   Answer: D. $172.80

   The 20% discount reduces the price by $48.00 to $192.00, and the additional 10% coupon reduces that new price by $19.20, resulting in a final price of $172.80. The value $168.00 is incorrect because it mistakenly adds the two percentages together for a single 30% discount off the original price. The value $192.00 is incorrect because it accounts only for the first discount and ignores the coupon.

3. Question 3 of 25Easy

   Given the function f(x) = 3x - 7, what is the value of f(-4)?

   1. AA. 5
   2. BB. -5
   3. CC. -19
   4. DD. 19
   Show answer to question 3

   Answer: C. -19

   Substitute -4 for x to get 3(-4) - 7 = -12 - 7 = -19. A common mistake is misinterpreting the subtraction of 7 from -12 as -5 by incorrectly treating the numbers as having opposite signs.

4. Question 4 of 25Medium

   A line graph shows the amount of water in a tank as it drains. The horizontal axis is time in minutes, and the vertical axis is water in gallons. The line passes through (0, 50) and (20, 10). At what rate is the water leaving the tank?

   1. AA. 2.5 gallons per minute
   2. BB. 50 gallons per minute
   3. CC. 2 gallons per minute
   4. DD. 40 gallons per minute
   Show answer to question 4

   Answer: C. 2 gallons per minute

   The rate is the slope: change in gallons divided by change in minutes, or (10 - 50) / (20 - 0) = -2. The water is leaving at 2 gallons per minute. The value 2.5 gallons per minute comes from dividing the starting 50 gallons by 20 minutes, which is not the rate of change.

5. Question 5 of 25Easy

   The side wall of a storage shed is composed of a rectangular section topped by a triangular gable. The rectangular section is 10 feet wide and 8 feet tall. The triangular section shares the 10-foot width as its base and has a height of 4 feet. What is the total area of the side wall in square feet?

   1. AA. 60
   2. BB. 120
   3. CC. 84
   4. DD. 100
   Show answer to question 5

   Answer: D. 100

   The total area is found by adding the area of the rectangle (10 feet multiplied by 8 feet, which equals 80 square feet) to the area of the triangle (one-half of 10 feet multiplied by 4 feet, which equals 20 square feet), yielding 100 square feet. The value 120 square feet is incorrect because it forgets to multiply the triangle's base and height by one-half.

6. Question 6 of 25Medium

   Which expression is equivalent to 8a^3b - 12a^2b^2 + 20ab when factored completely?

   1. AA. 4ab(2a^2 - 3ab + 5ab)
   2. BB. 2ab(4a^2 - 6ab + 10)
   3. CC. 4ab(2a^2 - 3ab)
   4. DD. 4ab(2a^2 - 3ab + 5)
   Show answer to question 6

   Answer: D. 4ab(2a^2 - 3ab + 5)

   The greatest common factor of all three terms is 4ab. Dividing each term by 4ab yields 2a^2 - 3ab + 5, so the complete factorization is 4ab(2a^2 - 3ab + 5). The expression 2ab(4a^2 - 6ab + 10) is a common error resulting from not factoring out the greatest numerical factor.

7. Question 7 of 25Medium

   An art instructor purchases supplies for 8 students. Each student receives a sketchbook that costs d dollars and a marker set that costs $6. The instructor also purchases a shared supply bin for the classroom that costs $25. Which expression represents the total cost, in dollars, of the purchases?

   1. AA. 8d + 48
   2. BB. 14d + 25
   3. CC. 8d + 73
   4. DD. 8d + 31
   Show answer to question 7

   Answer: C. 8d + 73

   Multiplying the 8 students by the sum of their individual supplies gives 8(d + 6), which expands to 8d + 48. Adding the $25 classroom supply bin gives 8d + 48 + 25, which simplifies to 8d + 73. The expression 8d + 31 is incorrect because the factor of 8 was only applied to the variable d instead of being distributed to both d and the $6 marker set.

8. Question 8 of 25Medium

   A plumber charges an initial service fee plus an hourly rate. The table below shows the total cost, y, for different numbers of hours worked, x. Hours Worked (x): 2, 5, 8, 11 Total Cost (y): $135, $240, $345, $450 What is the plumber's hourly rate?

   1. AA. $67.50 per hour
   2. BB. $45 per hour
   3. CC. $35 per hour
   4. DD. $105 per hour
   Show answer to question 8

   Answer: C. $35 per hour

   The hourly rate is the slope, found by dividing the change in total cost by the change in hours worked: (240 - 135) / (5 - 2) = 105 / 3 = $35 per hour. The rate of $105 per hour represents the total price change across consecutive rows without dividing by the 3-hour interval, while $67.50 incorrectly divides total cost by hours worked, ignoring the initial fixed fee.

9. Question 9 of 25Medium

   A rectangular room measures 4 1/2 inches by 3 inches on a floor plan. The scale is 1/4 inch = 1 foot. What is the actual area of the room?

   1. AA. 864 square feet
   2. BB. 60 square feet
   3. CC. 54 square feet
   4. DD. 216 square feet
   Show answer to question 9

   Answer: D. 216 square feet

   The plan dimensions convert to 18 feet by 12 feet, so the area is 18 * 12 = 216 square feet. The value 54 square feet comes from applying the linear scale once to the plan area instead of squaring the scale factor for area.

10. Question 10 of 25Medium

    A linear function is f(x) = 2x + 6. A nonlinear function is g(x) = x^2 + 2. Compare their average rates of change over the interval from x = 2 to x = 5. Which statement is true?

    1. AA. The average rate of change of f is greater.
    2. BB. The average rates of change are equal.
    3. CC. The average rate of change of g is greater.
    4. DD. The average rate of change cannot be compared because g is nonlinear.
    Show answer to question 10

    Answer: C. The average rate of change of g is greater.

    For f, the average rate of change over the interval is the slope 2. For g, the average rate is (27 - 6) / 3 = 7, which is greater. A nonlinear function still has an average rate of change over an interval, so the comparison can be made.

11. Question 11 of 25Hard

    A small model rocket is launched upward from a platform. Its height, h, in feet after t seconds is modeled by the equation h = -16t^2 + 60t + 5. How many seconds will it take for the rocket to hit the ground (h = 0)? Round to the nearest tenth of a second.

    1. AA. 1.9 seconds
    2. BB. 7.7 seconds
    3. CC. 3.8 seconds
    4. DD. 3.7 seconds
    Show answer to question 11

    Answer: C. 3.8 seconds

    Setting h = 0 and applying the quadratic formula yields t = (-60 ± √3920) / -32. Using the negative root in the numerator gives t = -122.61 / -32, which rounds to 3.8 seconds. The option of 1.9 seconds is incorrect because it represents the time to reach maximum height (-b / 2a) rather than the time to hit the ground, and 3.7 seconds is incorrect due to subtracting 320 rather than adding it under the radical.

12. Question 12 of 25Easy

    A cylindrical water storage tank has a diameter of 8 feet and a height of 15 feet. What is the volume of the tank in cubic feet? (Use 3.14 for pi.)

    1. AA. 753.6
    2. BB. 188.4
    3. CC. 251.2
    4. DD. 3,014.4
    Show answer to question 12

    Answer: A. 753.6

    To find the volume of a cylinder, first find the radius by dividing the diameter by 2, giving 4 feet. Then apply the volume formula by multiplying 3.14 by the square of the radius (16) and by the height (15), which yields 753.6 cubic feet. The value 3,014.4 results from mistakenly using the diameter instead of the radius in the formula.

13. Question 13 of 25Easy

    A delivery driver traveled 165 miles in the afternoon. This distance was 28 miles less than the morning route, represented by the equation m - 28 = 165, where m is the distance in miles driven in the morning. What is the value of m?

    1. AA. 193
    2. BB. 137
    3. CC. 183
    4. DD. 203
    Show answer to question 13

    Answer: A. 193

    To solve for m, add 28 to both sides of the equation, which gives 165 + 28 = 193. The value 137 is incorrect because it results from subtracting 28 from 165 instead of applying the inverse operation of addition.

14. Question 14 of 25Hard

    Wildlife biologists capture, tag, and release 120 trout into a lake. Several weeks later, they catch a random sample of 250 trout from the lake and find that 15 of them have tags. Based on this sample, what is the best estimate of the total trout population in the lake?

    1. AA. 1,800 trout
    2. BB. 2,000 trout
    3. CC. 1,500 trout
    4. DD. 2,500 trout
    Show answer to question 14

    Answer: B. 2,000 trout

    The ratio of tagged trout in the sample to the total sample equals the ratio of all tagged trout to the entire population: 15 / 250 = 120 / P. Solving for P gives (120 * 250) / 15 = 2,000 trout. Multiplying the original 120 tagged trout by the 15 tagged trout found in the sample yields 1,800 trout, which is an incorrect operation rather than setting up a proportional relationship.

15. Question 15 of 25Hard

    What is the value of y in the solution to the system of equations below? 3x + 4y = 1 2x - 3y = 12

    1. AA. 2
    2. BB. -2
    3. CC. 3
    4. DD. -3
    Show answer to question 15

    Answer: B. -2

    Multiplying the first equation by 2 and the second by 3 yields 6x + 8y = 2 and 6x - 9y = 36; subtracting these equations produces 17y = -34, so y = -2. The value 2 is incorrect because it results from a sign error when subtracting 36 from 2, and 3 is the value of x rather than y.

16. Question 16 of 25Hard

    Simplify: (7m^3 - 4m + 6) - (2m^3 + 5m^2 - 9m + 1).

    1. AA. 5m^3 - 5m^2 + 5m + 5
    2. BB. 5m^3 + 5m^2 + 5m + 5
    3. CC. 5m^3 - 5m^2 - 13m + 5
    4. DD. 5m^3 - 5m^2 + 5m + 7
    Show answer to question 16

    Answer: A. 5m^3 - 5m^2 + 5m + 5

    After the subtraction is distributed, the expression is 7m^3 - 4m + 6 - 2m^3 - 5m^2 + 9m - 1, and combining like terms gives 5m^3 - 5m^2 + 5m + 5. The result with +5m^2 occurs when the sign of 5m^2 is not changed during subtraction.

17. Question 17 of 25Easy

    Which expression is equivalent to (4x^5)(3x^(-8))?

    1. AA. 12x^3
    2. BB. 12 / x^3
    3. CC. 12 / x^40
    4. DD. 7 / x^3
    Show answer to question 17

    Answer: B. 12 / x^3

    To multiply expressions with the same base, multiply the coefficients (4 * 3 = 12) and add the exponents (5 + (-8) = -3), which gives 12x^(-3) or 12 / x^3. The option 12x^3 is incorrect because it subtracts 5 from 8 rather than adding 5 and -8. The option 7 / x^3 results from adding rather than multiplying the numerical coefficients.

18. Question 18 of 25Easy

    A delivery driver recorded the daily mileage for six consecutive days: 84, 92, 78, 95, 88, and 91 miles. What is the median daily mileage?

    1. AA. 86.5
    2. BB. 91.0
    3. CC. 88.0
    4. DD. 89.5
    Show answer to question 18

    Answer: D. 89.5

    To find the median, first arrange the numbers in order from least to greatest: 78, 84, 88, 91, 92, and 95. Because the set has an even number of values, calculate the mean of the two central numbers, 88 and 91, which gives 89.5. The value 86.5 is incorrect because it comes from averaging the middle two numbers of the list before arranging them in order.

19. Question 19 of 25Hard

    What is the value of the expression (3x^2 - 2xy) / (x - y) when x = -4 and y = -2?

    1. AA. 32
    2. BB. -16
    3. CC. 16
    4. DD. -32
    Show answer to question 19

    Answer: B. -16

    In the numerator, 3(-4)^2 = 3(16) = 48, and 2(-4)(-2) = 16, giving 48 - 16 = 32. In the denominator, -4 - (-2) = -2, and dividing 32 by -2 yields -16. The value 16 results from a sign error when computing the denominator as positive 2 instead of -2.

20. Question 20 of 25Hard

    A store marks up the wholesale price of an item by 40%. Later, the store discounts the marked price by 25%. What is the net percent change from the wholesale price to the final price?

    1. AA. 5% decrease
    2. BB. 5% increase
    3. CC. 15% increase
    4. DD. 10% increase
    Show answer to question 20

    Answer: B. 5% increase

    Using $100 as the wholesale price, a 40% markup makes the marked price $140. A 25% discount on $140 lowers it by $35 to $105, which is a 5% increase over the original $100. Subtracting 25% from 40% to get a 15% increase ignores that the discount is taken from the larger marked price.

21. Question 21 of 25Hard

    A veterinarian examined 75 animals on Monday and 90 animals on Tuesday. On Monday, 45 of the animals were dogs, and the rest were cats. On Tuesday, 60 of the animals were dogs, and the rest were cats. Which statement correctly compares the simplified ratio of dogs to cats seen on Monday to the simplified ratio of dogs to cats seen on Tuesday?

    1. AA. Monday was 3 to 2 and Tuesday was 2 to 1, so Tuesday had the higher ratio of dogs to cats.
    2. BB. Monday was 2 to 3 and Tuesday was 1 to 2, so Monday had the higher ratio of dogs to cats.
    3. CC. Monday was 3 to 2 and Tuesday was 3 to 2, so both days had an equal ratio of dogs to cats.
    4. DD. Monday was 3 to 5 and Tuesday was 2 to 3, so Tuesday had the higher ratio of dogs to cats.
    Show answer to question 21

    Answer: A. Monday was 3 to 2 and Tuesday was 2 to 1, so Tuesday had the higher ratio of dogs to cats.

    On Monday, there were 45 dogs and 30 cats (75 - 45), which simplifies to a ratio of 3 to 2, or 1.5. On Tuesday, there were 60 dogs and 30 cats (90 - 60), which simplifies to a ratio of 2 to 1, or 2.0, so Tuesday had the higher ratio. The statement with ratios 3 to 5 and 2 to 3 is incorrect because it compares the number of dogs to the total number of animals rather than the number of dogs to cats.

22. Question 22 of 25Medium

    A 20-foot ladder rests against the exterior wall of a house. The base of the ladder is placed 6 feet away from the base of the wall on level ground. To the nearest tenth of a foot, how high up the wall does the ladder reach?

    1. AA. 19.1 feet
    2. BB. 14.0 feet
    3. CC. 20.9 feet
    4. DD. 26.0 feet
    Show answer to question 22

    Answer: A. 19.1 feet

    The ladder represents the hypotenuse of a right triangle, while the ground distance represents one leg. Subtracting the square of the ground distance from the square of the ladder length gives 400 - 36 = 364, and the square root of 364 is approximately 19.1 feet. The choice of 20.9 feet is incorrect because it adds the squares instead of subtracting the leg square from the hypotenuse square.

23. Question 23 of 25Medium

    A graph contains the points (1, 2), (2, 3), (3, 4), and (2, 5). Which statement is correct?

    1. AA. The graph represents a function because the points can be joined by a smooth curve.
    2. BB. The graph does not represent a function because the input 2 has two different outputs.
    3. CC. The graph represents a function because all four y-values are different.
    4. DD. The graph does not represent a function because the points do not lie on a straight line.
    Show answer to question 23

    Answer: B. The graph does not represent a function because the input 2 has two different outputs.

    A function requires each input to have exactly one output. The input 2 is paired with both 3 and 5, so the graph is not a function. The distractor about all y-values being different confuses the output condition with the input condition; functions may have repeated y-values.

24. Question 24 of 25Medium

    An employee works 37.5 hours during a workweek at a pay rate of $16.40 per hour. From the weekly earnings, the employer deducts $86.25 for federal income tax, $38.13 for state income tax, and $47.05 for health insurance. What is the employee's take-home pay for that week?

    1. AA. $443.57
    2. BB. $444.57
    3. CC. $615.00
    4. DD. $481.70
    Show answer to question 24

    Answer: A. $443.57

    The employee earns a gross pay of $615.00 by multiplying 37.5 hours by $16.40. The total deductions equal $86.25 + $38.13 + $47.05 = $171.43. Subtracting the total deductions from the gross earnings gives a take-home pay of $443.57. An answer of $615.00 reflects only the gross pay before deductions, while $444.57 is the result of a subtraction regrouping error.

25. Question 25 of 25Medium

    What is the solution to the inequality 2(x - 5) >= 5x + 8, and how is it represented on a number line?

    1. AA. x >= -6, represented by a solid circle at -6 with an arrow pointing to the right
    2. BB. x >= 6, represented by an open circle at 6 with an arrow pointing to the right
    3. CC. x <= -6, represented by a solid circle at -6 with an arrow pointing to the left
    4. DD. x <= -6, represented by an open circle at -6 with an arrow pointing to the left
    Show answer to question 25

    Answer: C. x <= -6, represented by a solid circle at -6 with an arrow pointing to the left

    Distributing gives 2x - 10 >= 5x + 8, which simplifies to -3x >= 18 and yields x <= -6 after dividing by -3 and flipping the inequality symbol. On a number line, a non-strict inequality (<=) requires a solid circle at -6 with shading directed to the left. The option showing x >= -6 is incorrect because it overlooks the requirement to reverse the inequality sign when dividing by negative three.

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