Högskoleprovet (Sweden) · Quantitative Reasoning

Number, Algebra, Data Sufficiency and Probability

116 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 116 questions

  1. A jacket costs 800 kr. During a sale its price is reduced by 25%. What is the sale price?
  2. Solve the equation .
  3. What is the next number in the sequence 3, 7, 11, 15, ... ?
  4. A train travels 240 km in 3 hours at a constant speed. How far does it travel in 5 hours at the same speed?
  5. What is the mean of the numbers 4, 8, 9 and 15?
  6. A rectangle has an area of 48 cm and a width of 6 cm. What is its perimeter?
  7. What is 40% of 250?
  8. Simplify .
  9. How many minutes are there in 2.5 hours?
  10. What is the median of the numbers 9, 2, 12, 4 and 3?
  11. Two angles of a triangle are 50 degrees and 65 degrees. What is the third angle?
  12. What is the next number in the sequence 2, 6, 18, 54, ... ?
  13. A recipe for 4 people uses 300 g of rice. How much rice is needed for 10 people at the same rate?
  14. A price rises by 20% and the new price then falls by 20%. How does the final price compare with the original?
  15. A bag holds 3 red, 5 blue and 2 green marbles. One marble is drawn at random. What is the probability that it is red?
  16. A right triangle has legs of 9 cm and 12 cm. What is the length of the hypotenuse?
  17. Given and , what is the value of ?
  18. A car uses 6 litres of fuel per 100 km. How much fuel does it use on a 350 km journey?
  19. What is the value of ?
    (1)
    (2)
    Is the value of determined?
  20. Is the integer even?
    (1) is divisible by 3.
    (2) is odd.
  21. Compare A = and B = 0.4. Which statement is correct?
  22. In a class of 30 pupils, 40% are boys. A quarter of the boys wear glasses. How many boys wear glasses?
  23. A circle has a diameter of 10 cm. What is its area?
  24. What is the value of ?
  25. What is the next number in the sequence 2, 5, 10, 17, 26, ... ?
  26. One pipe fills a tank in 6 hours and another pipe fills the same tank in 3 hours. How long do they take together?
  27. A loan of 5,000 kr carries simple interest of 4% per year. How much interest is paid after 3 years?
  28. A shop mixes 2 kg of coffee at 90 kr/kg with 3 kg of coffee at 140 kr/kg. What is the price per kg of the mixture?
  29. Anna is three times as old as Bo. In 12 years Anna will be twice as old as Bo. How old is Bo now?
  30. Of 40 students, 25 study French, 18 study Spanish and 5 study neither. How many study both languages?
  31. The equation has two solutions. What is the sum of their squares?
  32. A cyclist rides to a town at 20 km/h and returns on the same road at 30 km/h. What is the average speed for the whole trip?
  33. A rectangle's length is increased by 50% and its width is decreased by 20%. How does its area change?
  34. Two marbles are drawn without replacement from a bag of 3 red and 5 blue marbles. What is the probability that both are red?
  35. A club of 5 members chooses a chair and a different member as deputy. How many different choices of the pair (chair, deputy) are possible?
  36. If and , what is ?
  37. The price of a camera is 100. It is first increased by 20% and then the new price is decreased by 25%. What is the final price?
  38. A grant of 25 is shared in the ratio . How much does the larger share receive?
  39. The mean of 4 numbers is 72. Of them, 3 are 77, 69, 84. What is the remaining number?
  40. One pipe fills a cistern in 6 hours and another pipe fills it in 12 hours. How many hours does it take to fill the cistern when both pipes are open?
  41. What is the difference between the compound interest and the simple interest on 2500 for 2 years at 6% per year (compounded annually)?
  42. A rectangle has length 5 cm and width 7 cm. A square of side 1 cm is cut from one corner. What is the area of the remaining shape, in cm?
  43. A right triangle has legs of length 9 and 12. What is the length of its hypotenuse?
  44. A box contains 5 red and 4 blue beads. Two beads are drawn at random without replacement. What is the probability that both are red?
  45. In how many ways can a team of 3 people be chosen from a group of 6 people?
  46. The equation has two roots. What is the sum of the squares of the roots?
  47. If and , what is ?
  48. An arithmetic sequence has first term 5 and common difference 5. What is the sum of its first 12 terms?
  49. How many integers satisfy ?
  50. On a map with scale 1 : 100000, two towns are 3 cm apart. What is the real distance in kilometres?
  51. A father is three times as old as his son. In 5 years the father's age will be 7 more than twice the son's age. How old is the son now?
  52. What is the median of the numbers 11, 15, 16, 7, 9, 11, 10, 28, 27?
  53. A line passes through the points and . What is its slope?
  54. What is the sum of the interior angles of a convex polygon with 9 sides?
  55. A cylinder has radius 9 cm and height 8 cm. What is its volume, in cm, in terms of ?
  56. A shop buys a jacket for 300, marks it up by 25% and then sells it at a 10% discount on the marked price. What is the profit (negative if a loss)?
  57. What is the least common multiple of 24 and 9?
  58. If and , what is ?
  59. How many integers from 1 to 70 are divisible by 6 or by 4 (or both)?
  60. If , what is the value of ?
  61. The price of a sofa is 200. It is first increased by 10% and then the new price is decreased by 50%. What is the final price?
  62. 60% of a number is 90. What is the number?
  63. The mean of 4 numbers is 70. Of them, 3 are 63, 67, 72. What is the remaining number?
  64. A car travels from A to B at 40 km/h and returns along the same road at 60 km/h. What is the average speed for the whole trip, in km/h?
  65. What is the difference between the compound interest and the simple interest on 1000 for 3 years at 6% per year (compounded annually)?
  66. A rectangle has length 4 cm and width 8 cm. A square of side 2 cm is cut from one corner. What is the area of the remaining shape, in cm?
  67. A right triangle has legs of length 16 and 30. What is the length of its hypotenuse?
  68. A box contains 8 red and 6 blue beads. Two beads are drawn at random without replacement. What is the probability that both are red?
  69. In how many ways can a team of 4 people be chosen from a group of 9 people?
  70. The equation has two roots. What is the sum of the squares of the roots?
  71. If and , what is ?
  72. An arithmetic sequence has first term 4 and common difference 4. What is the sum of its first 17 terms?
  73. How many integers satisfy ?
  74. A father is three times as old as his son. In 5 years the father's age will be 4 more than twice the son's age. How old is the son now?
  75. What is the median of the numbers 8, 5, 3, 3, 3, 25, 7?
  76. A line passes through the points and . What is its slope?
  77. What is the sum of the interior angles of a convex polygon with 12 sides?
  78. A cylinder has radius 5 cm and height 8 cm. What is its volume, in cm, in terms of ?
  79. A shop buys a bicycle for 200, marks it up by 20% and then sells it at a 20% discount on the marked price. What is the profit (negative if a loss)?
  80. What is the least common multiple of 42 and 16?
  81. If and , what is ?
  82. How many integers from 1 to 32 are divisible by 5 or by 5 (or both)?
  83. If , what is the value of ?
  84. The price of a jacket is 500. It is first increased by 20% and then the new price is decreased by 50%. What is the final price?
  85. 45% of a number is 54. What is the number?
  86. A legacy of 20 is shared in the ratio . How much does the larger share receive?
  87. One pipe fills a barrel in 3 hours and another pipe fills it in 6 hours. How many hours does it take to fill the barrel when both pipes are open?
  88. What is the difference between the compound interest and the simple interest on 1000 for 2 years at 6% per year (compounded annually)?
  89. A rectangle has length 13 cm and width 9 cm. A square of side 3 cm is cut from one corner. What is the area of the remaining shape, in cm?
  90. A right triangle has legs of length 9 and 40. What is the length of its hypotenuse?
  91. A jar contains 6 red and 6 blue counters. Two counters are drawn at random without replacement. What is the probability that both are red?
  92. In how many ways can a panel of 3 people be chosen from a group of 5 people?
  93. An arithmetic sequence has first term 5 and common difference 7. What is the sum of its first 20 terms?
  94. How many integers satisfy ?
  95. On a map with scale 1 : 100000, two towns are 13 cm apart. What is the real distance in kilometres?
  96. A father is three times as old as his son. In 2 years the father's age will be 7 more than twice the son's age. How old is the son now?
  97. What is the median of the numbers 6, 26, 10, 23, 29, 3, 29, 7, 24?
  98. A line passes through the points and . What is its slope?
  99. What is the sum of the interior angles of a convex polygon with 11 sides?
  100. A cylinder has radius 5 cm and height 3 cm. What is its volume, in cm, in terms of ?

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