GED Mathematical Reasoning Preparation Course: Expressions, equations and inequalities

1. Question 1 of 17

   What is the value of 3x² − 2x + 5 when x = −2?

   • A21
   • B13
   • C45
   • D−3
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   Answer: A. 21

   3(−2)² = 3 × 4 = 12. −2(−2) = +4. Then 12 + 4 + 5 = 21.

2. Question 2 of 17

   A plumber charges $65 for a visit plus $90 for each hour of work. Which expression gives the cost for h hours?

   • A65 + 90h
   • B65h + 90h
   • C155h
   • D90 + 65h
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   Answer: A. 65 + 90h

   The $65 is charged once, and the $90 is charged for each of the h hours: 65 + 90h.

3. Question 3 of 17

   Simplify: 4(x + 3) − 2(x − 5)

   • A2x + 22
   • B2x + 2
   • C6x + 22
   • D2x + 17
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   Answer: A. 2x + 22

   Distribute: 4x + 12 − 2x + 10. Note that −2 × −5 = +10. Combine: 2x + 22.

4. Question 4 of 17

   Solve: 5x − 7 = 3x + 9

   • Ax = −8
   • Bx = 8
   • Cx = 1/4
   • Dx = 1
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   Answer: B. x = 8

   Subtract 3x from both sides: 2x − 7 = 9. Add 7: 2x = 16. Divide by 2: x = 8.

5. Question 5 of 17

   Three consecutive whole numbers add up to 72. What is the smallest number?

   • A25
   • B22
   • C23
   • D24
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   Answer: C. 23

   Let the numbers be n, n + 1 and n + 2. Then 3n + 3 = 72, so 3n = 69 and n = 23.

6. Question 6 of 17

   Plan A costs $30 a month plus $0.10 per minute. Plan B costs $45 a month with unlimited minutes. For how many minutes do the plans cost the same?

   • A300
   • B450
   • C150
   • D75
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   Answer: C. 150

   Set 30 + 0.10m = 45. Then 0.10m = 15, so m = 150 minutes.

7. Question 7 of 17

   Solve the system: x + y = 12 and x − y = 4. What is x?

   • A6
   • B4
   • C16
   • D8
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   Answer: D. 8

   Add the two equations: 2x = 16, so x = 8. Then y = 12 − 8 = 4.

8. Question 8 of 17

   A school sold 20 tickets for $190. Adult tickets cost $12 and child tickets cost $7. How many adult tickets were sold?

   • A15
   • B10
   • C8
   • D12
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   Answer: B. 10

   Let a + c = 20 and 12a + 7c = 190. Replace c with 20 − a: 12a + 140 − 7a = 190, so 5a = 50 and a = 10.

9. Question 9 of 17

   Solve: 3x − 4 > 11

   • Ax > 5
   • Bx < 5
   • Cx > 15
   • Dx > 7/3
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   Answer: A. x > 5

   Add 4: 3x > 15. Divide by 3 (a positive number, so the sign stays): x > 5.

10. Question 10 of 17

    Solve: −2x + 6 ≤ 14

    • Ax ≤ 10
    • Bx ≥ 4
    • Cx ≥ −4
    • Dx ≤ −4
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    Answer: C. x ≥ −4

    Subtract 6: −2x ≤ 8. Dividing by −2 flips the sign: x ≥ −4.

11. Question 11 of 17

    Sam has $60. He pays $15 for a ticket and wants snacks that cost $4.50 each. What is the greatest number of snacks he can buy?

    • A9
    • B10
    • C11
    • D13
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    Answer: B. 10

    Write 15 + 4.50n ≤ 60. Then 4.50n ≤ 45, so n ≤ 10. He can buy at most 10 snacks.

12. Question 12 of 17

    Multiply: (2x + 3)(x − 4)

    • A2x² − 5x − 12
    • B2x² − 12
    • C2x² + 5x − 12
    • D2x² − 11x − 12
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    Answer: A. 2x² − 5x − 12

    Multiply each term: 2x·x = 2x², 2x·(−4) = −8x, 3·x = 3x, 3·(−4) = −12. Combine: 2x² − 5x − 12.

13. Question 13 of 17

    Factor: x² + 5x − 14

    • A(x + 7)(x − 2)
    • B(x − 7)(x + 2)
    • C(x + 7)(x + 2)
    • D(x + 14)(x − 1)
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    Answer: A. (x + 7)(x − 2)

    Find two numbers that multiply to −14 and add to 5: 7 and −2. So x² + 5x − 14 = (x + 7)(x − 2).

14. Question 14 of 17

    Simplify: (x² − 16) ÷ (x + 4)

    • Ax − 16
    • Bx² − 4
    • Cx + 4
    • Dx − 4
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    Answer: D. x − 4

    x² − 16 is a difference of squares: (x + 4)(x − 4). Divide out (x + 4) to get x − 4.

15. Question 15 of 17

    Solve: x² − 6x + 8 = 0

    • Ax = 2 or x = −4
    • Bx = −2 or x = −4
    • Cx = 1 or x = 8
    • Dx = 2 or x = 4
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    Answer: D. x = 2 or x = 4

    Factor: (x − 2)(x − 4) = 0. A product is 0 only if a factor is 0, so x = 2 or x = 4.

16. Question 16 of 17

    Use the quadratic formula to solve 2x² + 3x − 2 = 0.

    • Ax = −1/2 or x = 2
    • Bx = 1/2 or x = −2
    • Cx = 2 or x = −2
    • Dx = 1 or x = −4
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    Answer: B. x = 1/2 or x = −2

    a = 2, b = 3, c = −2. b² − 4ac = 9 + 16 = 25. x = (−3 ± 5) ÷ 4, so x = 2/4 = 1/2 or x = −8/4 = −2.

17. Question 17 of 17

    The formula d = rt gives distance from rate and time. Which formula gives the time t?

    • At = dr
    • Bt = r/d
    • Ct = d/r
    • Dt = d − r
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    Answer: C. t = d/r

    Divide both sides of d = rt by r: t = d/r. For example, 120 miles at 60 mph takes 2 hours.

Keyboard: 1–4 to answer, Enter for the next question.

The real test: 145 on each GED subject