FreeExam

ISEE Upper Quantitative Reasoning

Word problems and quantitative comparisons for students applying to grades 9 through 12, without a calculator.

ISEE is a registered trademark of E3n. FreeExam is not affiliated with E3n, and these questions are original practice, not an official test.

  1. 1.A winter coat costs $80. During a sale the price is reduced by 25%, and then a 10% sales tax is added to the sale price. What is the final cost, in dollars?

  2. 2.In a mosaic, red tiles and blue tiles are used in the ratio 3:5. The mosaic uses 24 red tiles. How many blue tiles does it use?

  3. 3.A savings jar starts with $3 and receives $5 each week. A second jar starts with $18 and receives $2 each week. After how many weeks do the jars hold the same amount?

  4. 4.A lab model gives the value -3x + 6, and that value must be greater than 15. Which inequality describes every x that works?

  5. 5.Two servers store 2^5 files and 2^3 files. Every file on the first server is paired with every file on the second. How many pairs are there?

  6. 6.A rectangular poster has area x^2 - 5x + 6. Which expression could be the length of one side?

  7. 7.A hiking trail on a coordinate map passes through (1, 2) and (4, 11), with units in kilometers. What is the slope of the trail?

  8. 8.A right triangular sail has edges of 9 feet and 12 feet that meet at a right angle. How long is the third edge, in feet?

  9. 9.A circular window has a radius of 6 feet. What is the area of the window, in terms of pi?

  10. 10.Two similar triangular signs have corresponding sides of 4 centimeters and 10 centimeters. The smaller sign has a perimeter of 18 centimeters. What is the perimeter of the larger sign, in centimeters?

  11. 11.On a 24-question quiz, Nia answers 18 questions correctly. What percent of the questions does she answer correctly?

  12. 12.A bakery recipe uses flour and sugar in the ratio 5:2. One batch uses 14 cups of sugar. How many cups of flour does that batch use?

  13. 13.Milo says that 3 times the result of subtracting 4 from a number x is 21. What is x?

  14. 14.A game gives 2 points for each level played and then subtracts a 5-point penalty. Which number of levels x leaves a score of at most 9?

  15. 15.A storage cube has volume 3^4 cubic units, and a smaller cube has volume 3^2 cubic units. How many more cubic units does the larger cube hold?

  16. 16.A rectangular garden has area x^2 + 7x + 12. Which product gives the side lengths of the garden?

  17. 17.A wheelchair ramp follows the line y = -2x + 5, where x is the horizontal distance and y is the height. What is the slope of the ramp?

  18. 18.A 5-meter pole stands upright. A taut wire runs from the top of the pole to a point on the ground 12 meters from the base. How long is the wire, in meters?

  19. 19.A circular fountain has a radius of 8 yards. What is the circumference of the fountain, in terms of pi?

  20. 20.Two garden plots are similar rectangles. The larger plot is a scale copy of the smaller plot with scale factor 3. The smaller plot has area 8 square meters. What is the area of the larger plot, in square meters?

  21. 21.The price of a concert ticket rises from $40 to $50. What is the percent increase?

  22. 22.A class has boys and girls in the ratio 4:7. There are 44 students. How many of the students are girls?

  23. 23.When 12 is added to a number, the result equals 3 times the number. What is the number?

  24. 24.Four friends each receive 1 more card than a number x, and together they have fewer than 20 cards. Which inequality describes every value of x that works?

  25. 25.A memory board contains (5^2)^3 cells. How many cells is that?

  26. 26.The area of a square of side x, minus the area of a square of side 7, is x^2 - 49. Which expression equals that difference?

  27. 27.A ski lift runs in a straight line through the points (0, -2) and (6, 4) on a grid measured in meters. What is the slope of the lift?

  28. 28.A rectangular field is 15 meters wide and 20 meters long. A straight path follows the diagonal. How long is the path, in meters?

  29. 29.A circular rug has a diameter of 10 feet. What is the area of the rug, in terms of pi?

  30. 30.A triangle has sides of 6, 8, and 10 inches. A similar triangle has a longest side of 25 inches. What is the shortest side of the larger triangle, in inches?

  31. 31.A theater has 250 seats, and 30% of the seats are reserved. How many seats are reserved?

  32. 32.On a trail map, 1 inch represents 8 miles. Two shelters are 3.5 inches apart on the map. How many miles apart are the shelters?

  33. 33.Half of a number, increased by 5, equals 13. What is the number?

  34. 34.A sensor reports an integer n such that -2 < n ≤ 4. How many possible readings are there?

  35. 35.A contest gives 5^0 points for entering and 2^3 bonus points for finishing. What is the total score?

  36. 36.A parabola's rule includes the expression x^2 - 2x - 15. Which product equals that expression?

  37. 37.A line on a city grid has slope 4 and passes through the point (2, 5). What is the y-intercept of the line?

  38. 38.A 13-foot ladder leans against a wall, with its base 5 feet from the wall. How many feet above the ground does the top of the ladder reach?

  39. 39.A circular track has circumference 18 pi meters. What is the radius of the track, in meters?

  40. 40.Two similar polygons have perimeters 12 and 30. One side of the smaller polygon is 4. What is the corresponding side of the larger polygon?

  41. 41.A club starts with 80 members. The number of members grows by 15%, and then 20 new members join. How many members does the club have then?

  42. 42.A painter mixes blue paint and yellow paint in the ratio 2:3. She uses 10 liters of blue paint. How many liters of paint are in the whole mixture?

  43. 43.Two notebooks cost x dollars each and three pens cost y dollars each, for a total of 18 dollars. Each pen costs 2 dollars. What is the cost of one notebook, in dollars?

  44. 44.A gauge reads 5 - 2x, and the reading must be at least 11. Which inequality describes every x that works?

  45. 45.A technician simplifies (8^2 × 2^2) / 4 before ordering supplies. What is that value?

  46. 46.A parabola crosses the horizontal axis where x^2 + 6x + 8 = 0. What is the greater x-intercept?

  47. 47.A road follows the line y = (1/2)x - 3. A service road is parallel to it. What is the slope of the service road?

  48. 48.A rectangular poster is 8 inches wide and 15 inches long. What is the length of a diagonal, in inches?

  49. 49.A circular patio has a radius of 4 yards. What is the circumference of the patio, in inches, in terms of pi?

  50. 50.A triangle has sides 9, 12, and 15. A smaller similar triangle is drawn with scale factor 1/3. What is the perimeter of the smaller triangle?

  51. 51.A lamp costs $50. The price is increased by 20%, and then that new price is decreased by 20%. What is the final price, in dollars?

  52. 52.A bus travels 180 miles in 2 hours and then 120 miles in 3 hours. What is the average speed for the whole trip, in miles per hour?

  53. 53.The sum of three consecutive integers is 72. What is the greatest of the three integers?

  54. 54.A square courtyard has area 100 square inches. A circle is drawn so that its diameter equals the side of the square. What is the area of the circle, in terms of pi?

  55. 55.Compare the two quantities. Column A: 25% of 80 Column B: 30% of 70

  56. 56.Compare the two quantities. Column A: 5^2 Column B: 3^3

  57. 57.Compare the two quantities. Column A: 7/8 Column B: 5/6

  58. 58.Compare the two quantities. Column A: 3(2 + 4) Column B: 2(2 + 7)

  59. 59.Compare the two quantities. Column A: the slope of the line through (1, 1) and (4, 7) Column B: the slope of the line through (0, 0) and (2, 5)

  60. 60.Compare the two quantities. x > 3 Column A: x Column B: 5

  61. 61.Compare the two quantities. Column A: y Column B: -y

  62. 62.Compare the two quantities. Column A: 3^4 Column B: 4^3

  63. 63.Compare the two quantities. Column A: x^2 - 9 Column B: (x - 3)(x + 3)

  64. 64.Compare the two quantities. Column A: x^2 Column B: x

  65. 65.Compare the two quantities. -4x < 8 Column A: -2 Column B: x

  66. 66.Compare the two quantities. Column A: 15% of 40 Column B: 10% of 60

  67. 67.Compare the two quantities. Column A: the hypotenuse of a right triangle with legs 6 and 8 Column B: 10

  68. 68.Compare the two quantities. Column A: 2/5 of 45 Column B: 3/4 of 28

  69. 69.Compare the two quantities. Column A: the solution of 4x - 8 = 12 Column B: 5

  70. 70.Compare the two quantities. Column A: -4 + 9 Column B: -2 + 9

  71. 71.Compare the two quantities. Column A: the perimeter of a square with side length 9 Column B: the perimeter of an equilateral triangle with side length 10

  72. 72.Compare the two quantities. Column A: 50% of 90 Column B: 40% of 100

  73. 73.Compare the two quantities. Column A: 2^3 × 2^2 Column B: 2^5

  74. 74.Compare the two quantities. Column A: the slope of the line y = -3x + 1 Column B: the slope of the line y = -x + 4

  75. 75.Compare the two quantities. Column A: the unknown leg of a right triangle with one leg 5 and hypotenuse 13 Column B: 13

  76. 76.Compare the two quantities. Column A: (1/3)^(-1) Column B: (1/2)^2

  77. 77.Compare the two quantities. xy = 12 and x > 0 Column A: x Column B: y

  78. 78.Compare the two quantities. Column A: 7 × 8 Column B: 9 × 6

  79. 79.Compare the two quantities. Column A: 3/2 + 1/4 Column B: 5/4

  80. 80.Compare the two quantities. Column A: 20% of 75 Column B: 15% of 100

  81. 81.Compare the two quantities. Column A: x + 3 Column B: 2x

  82. 82.Compare the two quantities. A rectangle has perimeter 20. Column A: the area of the rectangle Column B: 24

  83. 83.Compare the two quantities. Column A: 2^7 Column B: 5^3

  84. 84.Compare the two quantities. Column A: (x + 2)^2 Column B: x^2 + 4x + 4

  85. 85.Compare the two quantities. Column A: the distance between (0, 0) and (3, 4) Column B: 5

  86. 86.Compare the two quantities. a > 2 and b > 1 Column A: a + b Column B: ab

  87. 87.Compare the two quantities. Column A: 144 inches Column B: 4 yards

  88. 88.Compare the two quantities. Column A: the mean of 3, 9, 4, 7, and 2 Column B: the median of 3, 9, 4, 7, and 2

  89. 89.Compare the two quantities. 2 - x > 7 Column A: x Column B: -5

  90. 90.Compare the two quantities. Column A: 8/3 Column B: 5/2

  91. 91.Compare the two quantities. Column A: x Column B: |x|

  92. 92.Compare the two quantities. Column A: 35% of 20 Column B: 7

  93. 93.Compare the two quantities. Column A: the slope of the line through (-2, 1) and (2, 9) Column B: the slope of the line through (0, 0) and (5, 5)

  94. 94.Compare the two quantities. Column A: 4^3 + 4 Column B: 4^2 × 4

  95. 95.Compare the two quantities. x + y = 10 Column A: x Column B: 6

  96. 96.Compare the two quantities. n is an integer and n^2 < 20. Column A: n Column B: 4

  97. 97.Compare the two quantities. Column A: 2(3 + 5) Column B: 2 × 3 + 5

  98. 98.Compare the two quantities. x and y are positive numbers. Column A: x/y Column B: y/x

  99. 99.Compare the two quantities. Column A: 5^2 + 12^2 Column B: 13^2 - 1

  100. 100.Compare the two quantities. Column A: 1/2 + 1/3 Column B: 1/2 + 1/3 + 1/7

  101. 101.Compare the two quantities. Column A: -5 × 4 Column B: -5 × 3

  102. 102.Compare the two quantities. Column A: 40% of 40 Column B: 2^4

  103. 103.Compare the two quantities. Column A: the mean of 8, 12, and 16 Column B: the mean of 9, 12, and 18

  104. 104.Compare the two quantities. Column A: 3^5 Column B: 2^7

  105. 105.Compare the two quantities. Column A: 25% of 64 Column B: 20% of 90

  106. 106.Compare the two quantities. x < y Column A: x^2 Column B: y^2

  107. 107.Compare the two quantities. x = 4 Column A: 6x - 2x Column B: 3x + 1

  108. 108.Compare the two quantities. -3 < x < 2 Column A: x Column B: -x