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CLT Quantitative Reasoning

Arithmetic, algebra, geometry, trigonometry, logic, and word problems, without a calculator.

CLT is a registered trademark of Classic Learning Initiatives, LLC. FreeExam is not affiliated with Classic Learning Initiatives, LLC, and these questions are original practice, not an official test.

  1. 1.Every volunteer who staffs the book table also staffs the donation desk. Camille staffs the book table. Andre staffs the donation desk. No volunteer staffs both the book table and the coat check. Which statement must be true?

  2. 2.One angle of a triangle measures 48 degrees and another measures 67 degrees. What is the degree measure of the third angle?

  3. 3.Parallel lines m and n are cut by transversal t. One interior angle measures 118 degrees. What is the degree measure of the consecutive interior angle on the same side of t?

  4. 4.Solve 4x + 6 = 34 for x.

  5. 5.What is the value of 2^5 - 3^2?

  6. 6.A right triangle has acute angles of 30 degrees and 60 degrees. The side opposite the 30-degree angle has length 7. What is the length of the hypotenuse?

  7. 7.A bakery charges $3 for a muffin and $2 for a scone. Jordan buys 4 muffins and 6 scones. What is the total cost in dollars?

  8. 8.A delivery van travels 246 miles in 3 hours at a constant speed. What is that speed in miles per hour?

  9. 9.In an orchard the ratio of apple trees to pear trees is 2 to 7. There are 18 apple trees. How many pear trees are there?

  10. 10.Every painter in the studio uses oil paint. Nia uses oil paint. Leo is a painter in the studio. Which statement must be true?

  11. 11.If y = 3x - 5 and x = 4, what is y?

  12. 12.What is the midpoint of the segment with endpoints (2, 8) and (10, 4)?

  13. 13.A circle has radius 6. What is its area?

  14. 14.What is 3/4 + 5/6?

  15. 15.A clerk earns $15 an hour for the first 8 hours of a day and $22 an hour after that. The clerk works 11 hours. What is the day's pay in dollars?

  16. 16.Three stickers are in a row. The star is somewhere to the left of the moon, and the moon is somewhere to the left of the tree. Which statement must be true?

  17. 17.An isosceles right triangle has a leg of length 9. What is the length of the hypotenuse?

  18. 18.A class of 28 students has 3/7 of its members riding the morning bus. How many students ride that bus?

  19. 19.Solve 5(x - 2) = 35 for x.

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

  21. 21.A triangle has a base of 10 and a corresponding height of 6. What is its area?

  22. 22.Three friends split a $54 dinner bill in the ratio 1 to 2 to 3. What is the largest share in dollars?

  23. 23.What is the greatest common factor of 36 and 48?

  24. 24.No student in the morning section is also in the afternoon section. Jordan is in the morning section. Which statement must be true?

  25. 25.A pump moves 18 liters of water each minute. How many liters does it move in 25 minutes?

  26. 26.Which inequality is equivalent to 2x - 3 > 11?

  27. 27.What is the sum, in degrees, of the interior angles of a convex pentagon?

  28. 28.Two straight lines intersect and form a 35-degree angle. What is the degree measure of the angle that shares a side with it and forms a straight line?

  29. 29.A ladder leans against a vertical wall. Its foot is 5 feet from the wall, and the top rests 12 feet above the ground. How long is the ladder, in feet?

  30. 30.A jacket priced at $80 is discounted by 25 percent. A $6 coupon is then taken off the discounted price. What is the final price in dollars?

  31. 31.The courtyard gate opens only if the entry code is entered. Tonight the gate opens. Which statement must be true?

  32. 32.What is the least common multiple of 8 and 12?

  33. 33.If x + y = 16 and x - y = 6, what is y?

  34. 34.One exterior angle is taken at each vertex of a convex hexagon. What is the sum of those exterior angles, in degrees?

  35. 35.A rectangular patio is 14 feet by 9 feet. A flower box that is 2 feet by 3 feet sits on the patio and is not walked on. What is the walkable area in square feet?

  36. 36.A train covers 45 miles in 30 minutes at a steady speed. What is that speed in miles per hour?

  37. 37.No person seated in row 1 is wearing a hat. Mina is wearing a hat. Which statement must be true?

  38. 38.If sin θ = 3/5, what is cos² θ?

  39. 39.A shelf holds 9 rows of 8 jars. Five jars are then removed. How many jars remain?

  40. 40.The equation x² - 5x + 6 = 0 has two roots. What is the larger root?

  41. 41.What is the sum of the first six positive odd numbers?

  42. 42.A regular hexagon is drawn so that every vertex lies on a circle of radius 8. What is the perimeter of the hexagon?

  43. 43.A rectangular poster measures 3 feet by 2 feet. A copy is made so that every length is 4 times as long. What is the area of the copy, in square feet?

  44. 44.If it rains before noon, the match moves indoors. The match is being played outdoors. Which statement must be true?

  45. 45.A paint mix is 2 parts blue and 5 parts white. How many cups of blue paint are in 28 cups of the mix?

  46. 46.Museum tickets cost $12 for an adult and $7 for a child. A family buys 5 adult tickets and 3 child tickets. What is the total cost in dollars?

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

  48. 48.A hose adds 4 gallons of water per minute while an open drain removes 1 gallon per minute. How many minutes does it take for the water to increase by 36 gallons?

  49. 49.A right triangle has angles of 30, 60, and 90 degrees, and its hypotenuse is 20. What is the length of the longer leg?

  50. 50.What is the value of √144 + √25?

  51. 51.A rectangular banner is 16 inches wide and 5 inches tall. A triangular pennant with base 6 inches and height 5 inches is attached beside it, with no overlap. What is the combined area in square inches?

  52. 52.An isosceles triangle has a vertex angle of 40 degrees. The two base angles are equal. What is the degree measure of each base angle?

  53. 53.If a student takes ceramics, then that student takes studio art. If a student takes studio art, then that student has a locker on floor 2. Dana takes ceramics. Which statement must be true?

  54. 54.Eight pounds of rice cost $24. At the same price per pound, what is the cost of 5 pounds, in dollars?

  55. 55.An arithmetic sequence begins 7, 11, 15. What is the 8th term?

  56. 56.The soup of the day is either tomato or lentil, but not both. Today's soup is not tomato. Which statement must be true?

  57. 57.A semicircle has radius 4. What is its area?

  58. 58.What is the midpoint of the segment joining (-2, 5) and (8, -1)?

  59. 59.What is (2/3) times (9/4)?

  60. 60.A rectangular garden has a diagonal path that is 25 meters long and a width of 7 meters. What is the length of the garden, in meters?

  61. 61.Maya plants 6 shrubs an hour and Luis plants 4 shrubs an hour. Working at the same time for 3 hours, how many shrubs do they plant?

  62. 62.Solve 7x - 4 = 3x + 12 for x.

  63. 63.On a trail map, 1 inch represents 8 miles. A trail measures 7 inches on the map. How many miles long is the trail?

  64. 64.Exactly one of the red, blue, and green lockers is open. The blue locker is closed, and the green locker is closed. Which statement must be true?

  65. 65.What is the degree measure of each interior angle of a regular octagon?

  66. 66.In triangle ABC, angle A measures 42 degrees and angle B measures 61 degrees. Side BC is extended past C. What is the degree measure of the exterior angle at C?

  67. 67.A shop pays $28 for a lamp and $3 to ship it, then sells the lamp for $45. What is the profit in dollars?

  68. 68.What is the value of 3^4 ÷ 3^2?

  69. 69.Which inequality is equivalent to -4x > 20?

  70. 70.All of the blue bins are full. Some of the full bins are labeled. The east bin is blue. Which statement must be true?

  71. 71.An isosceles right triangle has hypotenuse 8√2. What is the length of each leg?

  72. 72.A parking row has 18 spaces, and 2/3 of them are filled. How many spaces are empty?

  73. 73.Two sides of a triangle have lengths 6 and 8. Which of the following can be the length of the third side?

  74. 74.A straight path on a coordinate map runs from (0, 0) to (9, 12). What is the length of the path?

  75. 75.A cyclist rides 12 miles in 40 minutes at a steady speed. What is that speed in miles per hour?

  76. 76.What is the smaller solution of (x - 4)(x + 3) = 0?

  77. 77.Rows of blocks use successive odd counts: row 1 has 1 block, row 2 has 3, row 3 has 5, and so on. How many blocks are in row 9?

  78. 78.Ada finishes before Ben, Ben finishes before Dee, and Dee finishes before Cho. Which statement must be true?

  79. 79.A taxi charges a $4 fee plus $2 for each mile. What is the cost, in dollars, of a 9-mile ride?

  80. 80.If cos θ = 5/13, what is sin² θ?

  81. 81.A quadrilateral has three angles measuring 85, 95, and 110 degrees. What is the degree measure of the fourth angle?

  82. 82.A rectangular floor is 12 feet by 10 feet. A square rug with side length 4 feet lies entirely on the floor. How many square feet of floor are uncovered?

  83. 83.If 2x + y = 13 and y = x + 1, what is x?

  84. 84.At a shelter the ratio of cats to dogs is 5 to 3. There are 24 dogs. How many cats are there?

  85. 85.A swimmer may enter the lake only when both a buddy is present and a whistle is worn. Rio enters the lake. Which statement must be true?

  86. 86.How many positive factors does 36 have?

  87. 87.A tailor cuts a ribbon that is 4 yards long into pieces that are 8 inches long. How many pieces does the tailor get?

  88. 88.A central angle of a circle measures 70 degrees. What is the degree measure of an inscribed angle that intercepts the same arc?

  89. 89.A trapezoid has parallel sides of length 10 and 16 and a height of 5. What is its area?

  90. 90.A printer produces 24 pages each minute. How many minutes does it need to produce 360 pages?

  91. 91.If a = -2, what is the value of a² - 3a?

  92. 92.A guy wire runs 29 feet from the top of a vertical pole to a stake. The stake is 20 feet from the base of the pole. How tall is the pole, in feet?

  93. 93.A password works only when it has both a digit and a capital letter. This password works, and it has a digit. Which statement must be true?

  94. 94.A baker makes 5 trays with 12 rolls on each tray, then gives away 9 rolls. How many rolls remain?

  95. 95.What is 7/8 - 1/2?

  96. 96.An equilateral triangle has perimeter 45. What is the length of one side?

  97. 97.A rectangular board is 20 inches by 8 inches. A right triangular piece with legs of 8 inches and 6 inches is cut from one corner and removed. What is the area, in square inches, of the board that remains?

  98. 98.Solve x/3 + 4 = 10 for x.

  99. 99.Every red marble in the jar is glass. None of the glass marbles are cracked. The marble in the box is red. Which statement must be true?

  100. 100.A hall sells 40 seats at $15 each and 20 seats at $25 each. What is the total sales amount in dollars?

  101. 101.A recipe uses 2 cups of oats for every 3 cups of flour. How many cups of oats are needed with 12 cups of flour?

  102. 102.Two sides of a right triangle meet at the right angle and measure 8 and 15. What is the length of the side opposite the right angle?

  103. 103.A rhombus has diagonals of lengths 10 and 8. What is its area?

  104. 104.What is the product of the even integers from 2 through 6 inclusive?

  105. 105.What is the negative solution of x² = 49?

  106. 106.A triangle has vertices at (2, 1), (2, 7), and (6, 1). What is its area?

  107. 107.At least one of these is true: the vase is blue, or the vase is tall. The vase is not tall. Which statement must be true?

  108. 108.A worker earns $18 an hour for 6 hours and spends $15 of that pay on lunch. How many dollars remain?