TMS (Test fßr Medizinische Studiengänge) practice ¡ Quantitative and Formal Problems

Percentages, Ratios and Formulas

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

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  1. A price falls by 20 percent and then rises by 25 percent. What is the net change?
  2. A test finds 90 of 100 people who have a disease. What is its sensitivity?
  3. A disease has a prevalence of 2 percent in a town of 10,000 people. How many people have it?
  4. In a group of 10,000 people, 200 have a disease. The test has a specificity of 95 percent. About how many healthy people test positive?
  5. A population of 1,000 grows by 10 percent per year. How large is it after two years?
  6. A vehicle covers 120 km at 60 km/h and then 120 km at 40 km/h. What is its average speed?
  7. Four workers finish a job in 6 days. How many days do three workers need, at the same rate?
  8. The mean of five numbers is 12. What must a sixth number be to raise the mean to 13?
  9. Solve for x: 3x - 7 = 11.
  10. A value rises from 240 to 300. What is the percentage increase?
  11. After a 20 percent discount an item costs 160 euros. What was the original price?
  12. Two independent events each have a probability of 0.3. What is the probability that both occur?
  13. A treatment lowers the risk of an event by 4 percentage points. How many patients must be treated to prevent one event (number needed to treat)?
  14. The risk of a disease is 10 percent in an exposed group and 5 percent in an unexposed group. What is the relative risk?
  15. A metal block has a mass of 540 g and a volume of 200 cubic centimetres. What is its density?
  16. A plan splits 250 euros in the ratio 2 to 3. What is the larger share?
  17. A pulse of 24 beats is counted in 20 seconds. What is the heart rate in beats per minute?
  18. A mixture of two liquids has the ratio 4 : 1. How many ml of the first liquid are in 75 ml of the mixture?
  19. A mixture of two liquids has the ratio 5 : 3. How many ml of the first liquid are in 160 ml of the mixture?
  20. A vehicle covers 150 km in 2.5 hours. What is its average speed?
  21. A value falls or rises from 50 to 65. By what percentage does it change (absolute value)?
  22. A mixture of two liquids has the ratio 3 : 2. How many ml of the first liquid are in 250 ml of the mixture?
  23. What is 15 % of 240?
  24. A vehicle covers 240 km in 4 hours. What is its average speed?
  25. Convert 40 degrees Celsius to degrees Fahrenheit using F = 1.8 x C + 32.
  26. Convert 20 degrees Celsius to degrees Fahrenheit using F = 1.8 x C + 32.
  27. A value falls or rises from 80 to 100. By what percentage does it change (absolute value)?
  28. Convert 25 degrees Celsius to degrees Fahrenheit using F = 1.8 x C + 32.
  29. Convert 37 degrees Celsius to degrees Fahrenheit using F = 1.8 x C + 32.
  30. A mixture of two liquids has the ratio 2 : 7. How many ml of the first liquid are in 90 ml of the mixture?
  31. The body mass index is the mass in kg divided by the square of the height in metres. What is the BMI of a person with 54 kg and 1.5 m?
  32. Convert 0 degrees Celsius to degrees Fahrenheit using F = 1.8 x C + 32.
  33. After a price reduction of 10 %, an article costs 45 euros. What was the original price?
  34. A pulse of 12 beats is counted in 10 seconds. What is the heart rate in beats per minute?
  35. The body mass index is the mass in kg divided by the square of the height in metres. What is the BMI of a person with 90 kg and 1.5 m?
  36. A sample has a mass of 250 g and a volume of 20 cm3. What is its density?
  37. What is 12 % of 450?
  38. A value falls or rises from 400 to 340. By what percentage does it change (absolute value)?
  39. A pulse of 18 beats is counted in 15 seconds. What is the heart rate in beats per minute?
  40. A pulse of 36 beats is counted in 30 seconds. What is the heart rate in beats per minute?
  41. A mixture of two liquids has the ratio 1 : 4. How many ml of the first liquid are in 100 ml of the mixture?
  42. A sample has a mass of 90 g and a volume of 10 cm3. What is its density?
  43. Convert 100 degrees Celsius to degrees Fahrenheit using F = 1.8 x C + 32.
  44. A value falls or rises from 200 to 150. By what percentage does it change (absolute value)?
  45. A vehicle covers 90 km in 1.5 hours. What is its average speed?
  46. A mixture of two liquids has the ratio 3 : 5. How many ml of the first liquid are in 240 ml of the mixture?
  47. What is 45 % of 60?
  48. What is 5 % of 320?
  49. After a price reduction of 25 %, an article costs 150 euros. What was the original price?
  50. After a price reduction of 10 %, an article costs 270 euros. What was the original price?
  51. A vehicle covers 45 km in 0.75 hours. What is its average speed?
  52. After a price reduction of 20 %, an article costs 80 euros. What was the original price?

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