FreeExam

GMAT Quantitative Reasoning: Algebra

Expressions, equations, inequalities, functions, and word problems set up as equations.

GMAT is a registered trademark of the Graduate Management Admission Council. FreeExam is not affiliated with the Graduate Management Admission Council, and these questions are original practice, not an official test.

  1. 1.Which expression is equivalent to 3(2x + 4) - 5x?

  2. 2.Simplify 4(x - 2) + 3(2x + 1).

  3. 3.After the minus sign is distributed, what is -2(3x - 5) + 4x?

  4. 4.Subtract the polynomials: (6x^2 - 4x + 9) - (2x^2 - 5x + 3).

  5. 5.Multiply, then combine like terms: 2x(x - 3) + 5x.

  6. 6.Expand the product (3x + 2)(x - 4).

  7. 7.For every x not equal to 0, which expression equals (8x^3 - 2x)/(2x)?

  8. 8.Combine like terms in 7y - 3(y - 4) + 2.

  9. 9.Which expression equals (x^2 + 6x + 8) - (x^2 - 2x + 5)?

  10. 10.If a = 4 and b = -2, what is the value of 2a - 3b?

  11. 11.Expand and simplify 5(2x^2 - x) - 3x(x - 4).

  12. 12.Which expression is equivalent to 9 - 4(2k - 1)?

  13. 13.The factors x^5 and x^3 are multiplied. Which power of x is the product?

  14. 14.The power (y^4)^3 is simplified. What is the result?

  15. 15.What is (2m^3)^2 in simplest form?

  16. 16.Where a is not 0, what is 12a^5 divided by 3a^2?

  17. 17.Multiply the monomials (3x^2 y)(2x y^3).

  18. 18.For every integer n and every k not equal to 0, k^(n + 2) / k^(n - 1) equals which expression?

  19. 19.For every p and q not equal to 0, simplify (4p^2 q^3)^2 / (2p q).

  20. 20.Where x is not 0, which power equals x^(-2) * x^5?

  21. 21.Where m and n are not 0, simplify (m^6 n^2) / (m^2 n^2).

  22. 22.Where x is not 0, what is (x^3)^2 * x^(-4)?

  23. 23.For every n, which expression equals 2^3 * 2^n?

  24. 24.For every t not equal to 0, simplify (6t^4 - 9t^2) / (3t^2).

  25. 25.Which product is a factorization of x^2 + 8x + 15?

  26. 26.Factor x^2 - 25 over the integers.

  27. 27.Which factorization equals 2x^2 + 5x + 2?

  28. 28.Factor x^2 - 3x - 18.

  29. 29.What is the complete factorization of 5x^2 + 15x?

  30. 30.Which expression equals the perfect square x^2 + 10x + 25?

  31. 31.Factor 6x^2 + 7x + 2.

  32. 32.Which product equals x^2 - x - 30?

  33. 33.Factor 9x^2 - 4.

  34. 34.Factor 2x^3 - 2x^2 - 12x completely.

  35. 35.Which binomial is a factor of x^2 + 4x - 21?

  36. 36.Which expression is a perfect-square factorization of 4x^2 + 12x + 9?

  37. 37.If 5x - 8 = 22, what is x?

  38. 38.What value of x satisfies 3(x - 4) = 2x + 5?

  39. 39.Which number makes x/5 + 2 equal 6?

  40. 40.Find x if 7x + 2 = 4x + 17.

  41. 41.Find the number x that satisfies 2(3x + 1) = 4(x + 5).

  42. 42.What is x if 8 - 2x = 14?

  43. 43.Solve 4(y + 2) - y = 23 for y.

  44. 44.Which number satisfies (2x - 1)/5 = 3?

  45. 45.What is x when (1/2)x + 6 = 10?

  46. 46.Find x in the equation 6x - 5 = 3x + 16.

  47. 47.Which inequality describes every x such that 3x + 4 > 19?

  48. 48.What is the solution of -2x + 6 <= 14?

  49. 49.Solve for x: 5 - x < 2.

  50. 50.Which values of x satisfy 4(x - 2) >= 12?

  51. 51.What is the solution of -3(x + 1) > 9?

  52. 52.Which inequality has the same solutions as 2x - 7 < 5x + 2?

  53. 53.Which inequality is equivalent to 6 <= 3x + 9?

  54. 54.What is the smallest integer x such that 2x + 1 > 11?

  55. 55.If -4x >= 20, what is true of x?

  56. 56.Which inequality is equivalent to 8 - 3x > 2?

  57. 57.Find all x such that x/2 - 3 <= 4.

  58. 58.Solve for x in the inequality 7x + 1 >= 2x - 14.

  59. 59.Adding the equations x + y = 15 and x - y = 3 eliminates y. What is x?

  60. 60.What is x in the pair of equations 3x + y = 14 and x - y = 2?

  61. 61.Two equations are x + 3y = 17 and x + y = 9. What is y?

  62. 62.The system 4x + y = 18 and 4x - y = 6 is solved for y. What is y?

  63. 63.One equation in a system is y = 6. The other is 4x + y = 22. What is x?

  64. 64.A pair of numbers adds to 8. Twice the first number plus the second number is 13. What is the product of the two numbers?

  65. 65.Subtracting 2x + y = 8 from 5x + y = 17 leaves an equation in x. What is y in the original system?

  66. 66.A number x is four times a number y, and x + y = 25. What is x?

  67. 67.In the system x + y = 7 and 4x + y = 19, what is x?

  68. 68.Solving 3x - y = 5 together with x + y = 7, what is y?

  69. 69.Small cups cost 2 dollars and large cups cost 5 dollars. A purchase of 8 cups costs 25 dollars. How many large cups were bought?

  70. 70.If 2x + y = 14 and y = x + 2, what is x?

  71. 71.The equation x^2 - 7x + 10 = 0 has two integer solutions. What are they?

  72. 72.Which pair solves x^2 + x - 12 = 0?

  73. 73.If x^2 = 64, which pair lists every solution?

  74. 74.Which values of x satisfy x^2 + 6x = 0?

  75. 75.Which pair satisfies x^2 - 2x - 24 = 0?

  76. 76.Of the two roots of x^2 - 9x + 18 = 0, which is larger?

  77. 77.The quadratic x^2 - 10x + 25 = 0 has one repeated root. What is it?

  78. 78.Which values satisfy 3x^2 - 15x = 0?

  79. 79.Find both solutions of x^2 + 3x - 18 = 0.

  80. 80.Which pair is the solution set of x^2 - x - 6 = 0?

  81. 81.Between the roots of x^2 + 9x + 14 = 0, which number is smaller?

  82. 82.What are all solutions of 2x^2 = 32?

  83. 83.If f(x) = 4x - 7, what is f(3)?

  84. 84.If g(x) = x^2 - 6x, what is g(4)?

  85. 85.If h(x) = 3x + 1 and h(x) = 16, what is x?

  86. 86.If p(n) = n^2 + n, what is p(4)?

  87. 87.If f(x) = 4 - x, what is f(-2)?

  88. 88.If f(x) = 2x + 3 and g(x) = x - 1, what is f(g(5))?

  89. 89.If f(x) = x^2 - 1, which expression equals f(a + 1)?

  90. 90.If f(x) = 5x - 2 and f(k) = 18, what is k?

  91. 91.If f(x) = x + 7, what is f(2) + f(3)?

  92. 92.If f(x) = x^2, which value other than 3 also satisfies f(x) = f(3)?

  93. 93.Which values satisfy |x| = 6?

  94. 94.The equation |x - 4| = 7 has two solutions. What are they?

  95. 95.If the absolute value of 2x is 10, what are the possible values of x?

  96. 96.Which pair solves |x + 4| = 1?

  97. 97.What number satisfies |x - 1| = 0?

  98. 98.Which values of x satisfy |3x + 6| = 9?

  99. 99.If |x| + 2 = 7, what are the possible values of x?

  100. 100.Which values of x make |4 - x| equal 6?

  101. 101.A jar starts with 4 tokens. Each pouch added to the jar contributes 3 tokens. After some pouches are added, the jar has 31 tokens. How many pouches were added?

  102. 102.Lena has 18 more stamps than Marco. Together they have 62 stamps. How many stamps does Marco have?

  103. 103.A repair visit costs 40 dollars plus 20 dollars for each hour of work. The bill is 140 dollars. How many hours were billed?

  104. 104.Two consecutive even integers add to 54. What is the smaller integer?

  105. 105.A tank starts with 40 liters. Water flows in at 6 liters per minute and drains at 2 liters per minute. After how many minutes does the tank contain 64 liters?

  106. 106.The sum of a number and three times that number is 48. What is the number?

  107. 107.Student tickets cost 8 dollars and adult tickets cost 12 dollars. Ten tickets cost 96 dollars in all. How many of the tickets are student tickets?

  108. 108.In 4 hours a cyclist rides 18 miles farther than in 2 hours, at one steady speed. What is that speed in miles per hour?