FreeExam

GRE Quantitative Reasoning: Algebra

Expressions, equations, inequalities, functions, and lines on the coordinate plane.

GRE is a registered trademark of Educational Testing Service. FreeExam is not affiliated with Educational Testing Service, and these questions are original practice, not an official test.

  1. 1.Simplify 5(2x - 3) - 4x.

  2. 2.Solve 4x - 7 = 21.

  3. 3.Which expression is equal to x^2 + 5x + 6?

  4. 4.Quantity A: (3x + 6)/3 Quantity B: x + 2

  5. 5.Solve 3x - 4 > 11.

  6. 6.Simplify (x^3)^2 * x^4.

  7. 7.In the system 2x + y = 11 and x - y = 1, what is y?

  8. 8.Quantity A: x^2 - 9 Quantity B: (x - 3)(x + 3)

  9. 9.If f(x) = 3x - 4, what is f(5)?

  10. 10.What are the solutions of |x - 3| = 8?

  11. 11.What is the slope of the line through (2, 1) and (6, 9)?

  12. 12.Quantity A: the slope of the line through (0, 0) and (4, 4) Quantity B: the slope of the line through (0, 0) and (2, 6)

  13. 13.What is the smaller solution of x^2 - 7x + 12 = 0?

  14. 14.A number increased by 9 equals 4 times the number. What is the number?

  15. 15.What is the midpoint of the segment joining (2, 8) and (10, 4)?

  16. 16.k is a real number. Quantity A: k + 2 Quantity B: 3k

  17. 17.Simplify (12x^3 y^2)/(3x y), where x and y are not 0.

  18. 18.Solve -2x > 10.

  19. 19.What is the distance between (1, 2) and (4, 6)?

  20. 20.Quantity A: (x + 1)^2 - (x - 1)^2 Quantity B: 4x

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

  22. 22.Which expression is equal to 2x^2 + 7x + 3?

  23. 23.Solve x/3 + 2 = 7.

  24. 24.n is an integer. Quantity A: n + 3 Quantity B: 2n

  25. 25.Simplify x^5 / x^2, where x is not 0.

  26. 26.If 3x + 2y = 16 and x = 2, what is y?

  27. 27.On the parabola y = x^2 - 4, what is y when x = 3?

  28. 28.3x + 2 = 14 Quantity A: x Quantity B: 5

  29. 29.What is the positive solution of |2x - 6| = 10?

  30. 30.A line has slope -2 and y-intercept 4. Which equation matches the line?

  31. 31.Twice a number, decreased by 5, equals 19. What is the number?

  32. 32.The line is y = 2x - 8. Quantity A: the x-intercept Quantity B: 4

  33. 33.Simplify 4(x + 3) - 2(x - 5).

  34. 34.Which number is a solution of x^2 + 2x - 15 = 0?

  35. 35.What is the y-intercept of the line 4x + 2y = 12?

  36. 36.f(x) = 2x + 1 Quantity A: f(3) Quantity B: f(4)

  37. 37.If g(x) = 5 - x, what is g(2) + g(0)?

  38. 38.Simplify (2x)^3.

  39. 39.Which value of x satisfies 5 <= 2x + 1 <= 13?

  40. 40.Quantity A: the distance between (0, 0) and (3, 4) Quantity B: 5

  41. 41.Which expression is equal to x^2 - 9?

  42. 42.Solve 7x - 3 = 4x + 9.

  43. 43.What is the x-intercept of the line y = 3x - 12?

  44. 44.A line has slope 2. Quantity A: the y-intercept of the line Quantity B: 3

  45. 45.Simplify (x^2)^3 * x^(-4).

  46. 46.If y = 2x and x + y = 12, what is x?

  47. 47.The length of a rectangle is 3 more than twice its width, and the perimeter is 36. What is the width?

  48. 48.x + y = 10 Quantity A: x Quantity B: y

  49. 49.What is the greater solution of |x + 4| = 2?

  50. 50.What is the distance between (0, 0) and (8, 6)?

  51. 51.If f(x) = x^2 + 1, what is f(f(1))?

  52. 52.x^2 = 16 Quantity A: x Quantity B: 0

  53. 53.What is the product of the solutions of x^2 - 6x + 8 = 0?

  54. 54.Which equation is the line of slope 1/2 through (2, 3)?

  55. 55.Solve 4 - x < 10.

  56. 56.xy = 12, and x and y are positive. Quantity A: x Quantity B: y

  57. 57.If 3^x = 81, what is x?

  58. 58.Expand and simplify 2x(x - 4) + 3(x - 4).

  59. 59.What is the midpoint of (-2, 5) and (6, -1)?

  60. 60.p(x) = 10 - x Quantity A: p(6) Quantity B: p(2)

  61. 61.If 4x - y = 7 and y = x + 2, what is y?

  62. 62.A ride costs 3 dollars plus 2 dollars per mile, and the total is 17 dollars. How many miles is the ride?

  63. 63.Which expression is equal to x^2 - 4x - 21?

  64. 64.|x - 2| = 5 Quantity A: x Quantity B: 0

  65. 65.What is the slope of the line 6x - 2y = 8?

  66. 66.What is the negative solution of |x| + 3 = 10?

  67. 67.If h(x) = -2x + 9, for which x is h(x) = 1?

  68. 68.x + y = 9 and x - y = 1 Quantity A: y Quantity B: x

  69. 69.What is the larger solution of x^2 - 9x + 20 = 0?

  70. 70.A line is parallel to y = 4x - 1. What is its slope?

  71. 71.Expand (x + 5)^2.

  72. 72.The point (a, b) lies on the line y = 2x. Quantity A: a Quantity B: b

  73. 73.Solve 2(x - 3) <= 8.

  74. 74.Simplify (x^4 y^2)^2 / (x y), where x and y are not 0.

  75. 75.Two numbers add to 20, and the larger is 6 more than the smaller. What is the larger number?

  76. 76.Quantity A: the x-coordinate of the midpoint of (0, 0) and (6, 8) Quantity B: the y-coordinate of that midpoint

  77. 77.The line y - 2 = 3(x - 1) passes through x = 4. What is y there?

  78. 78.If 2x + 3y = 12 and 2x - 3y = 0, what is x + y?

  79. 79.What is the y-intercept of the parabola y = (x - 2)^2?

  80. 80.x > 4 Quantity A: x Quantity B: 10

  81. 81.What is the sum of the solutions of |3x + 3| = 9?

  82. 82.Which expression is equal to 6x^2 + 11x + 3?

  83. 83.What is the distance between (2, -1) and (2, 5)?

  84. 84.2^x = 16 Quantity A: x Quantity B: 5

  85. 85.Solve (2/3)x = 8.

  86. 86.If f(x) = 4x - x^2, what is f(1)?

  87. 87.Solve -x/2 >= 3.

  88. 88.Quantity A: (2x)^2 Quantity B: 4x^2

  89. 89.What is the slope of the line through (5, 7) and (9, 7)?

  90. 90.A book costs 8 dollars more than a pen. Together they cost 26 dollars. What is the price of the pen, in dollars?

  91. 91.Simplify 8x - 3(2x - 4).

  92. 92.x + 2y = 8 Quantity A: x Quantity B: y

  93. 93.What is the negative solution of x^2 + x - 6 = 0?

  94. 94.Which equation is the line through (0, -1) and (3, 5)?

  95. 95.What is the product of the solutions of |2x + 1| = 7?

  96. 96.Quantity A: the slope of the line through (0, 0) and (2, 6) Quantity B: 1

  97. 97.Two notebooks and one pen cost 11 dollars. One notebook and one pen cost 7 dollars. What is the cost of one notebook, in dollars?

  98. 98.Which expression equals 2^3 * 2^4?

  99. 99.What is the y-coordinate of the midpoint of (3, 10) and (3, -2)?

  100. 100.Solve 6x + 1 >= 4x + 9.

  101. 101.If f(x) = x^3 - x, what is f(2)?

  102. 102.Which expression is equal to 3x^2 - 12?

  103. 103.What is the slope of a line perpendicular to a line of slope 2?

  104. 104.Three consecutive integers add to 51. What is the smallest of the three?

  105. 105.Solve (x - 2)/5 = 3.

  106. 106.What is the solution of x^2 + 8x + 16 = 0?

  107. 107.Simplify (5x^2 - 10x)/(5x), where x is not 0.

  108. 108.A line has y-intercept 6 and passes through (2, 2). What is its slope?