Bangladesh Civil Service Preliminary Examination · Mathematical Reasoning and Mental Ability

Arithmetic, Number Systems and Percentages

35 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 35 questions

  1. How many prime numbers exist between 1 and 50 inclusive?
  2. The product of two positive integers is 840, and their Highest Common Factor (HCF) is 4. What is their Least Common Multiple (LCM)?
  3. Which of the following fractions has the greatest numerical value: 3/5, 7/10, 11/15, or 4/5?
  4. An amount of 1,200 BDT is divided among three persons A, B, and C in the ratio 3 : 4 : 5. What is the monetary share of B?
  5. What is the compound ratio of the three simple ratios 2 : 3, 6 : 5, and 10 : 9?
  6. If the market price of sugar increases by 25%, by what percentage must a household reduce its consumption to keep total expenditure unchanged?
  7. The population of a municipal town is currently 50,000 and grows at a steady rate of 4% per annum. What will the population be after 2 years?
  8. A trader purchases an article for 800 BDT and sells it for 960 BDT. What is the percentage profit on the transaction?
  9. What single discount percentage is equivalent to two successive discounts of 20% and 10%?
  10. Calculate the simple interest on a principal of 6,000 BDT invested at 8% per annum for a period of 3 years.
  11. In how many years will a sum of money double itself under simple annual interest at an interest rate of 10% per annum?
  12. What is the compound interest earned on 5,000 BDT at 10% per annum for 2 years compounded annually?
  13. What is the difference between compound interest and simple interest on a principal of 4,000 BDT at 5% per annum for 2 years?
  14. Worker A can complete a construction task in 12 days, while Worker B can complete the same task in 18 days. Working together, in how many days can they finish the task?
  15. Worker A is twice as efficient as Worker B. Working together, they complete a job in 14 days. In how many days can Worker A alone complete the entire job?
  16. Pipe A can fill a water reservoir in 20 minutes and Pipe B can fill it in 30 minutes. If both pipes are opened simultaneously, how long does it take to fill the reservoir?
  17. An inlet pipe can fill a cistern in 6 hours, but due to a leak at the bottom, it takes 8 hours to fill. How long will the leak take to empty a full cistern when the inlet is closed?
  18. A vehicle travels a distance of 120 km at 60 km/h and an additional 270 km at 90 km/h. What is the average speed of the vehicle over the entire journey?
  19. Express a velocity of 72 kilometers per hour in meters per second.
  20. A passenger train 180 meters in length travels at a constant speed of 54 km/h. How many seconds does it take to pass a stationary signal post?
  21. A train 150 meters long traveling at 72 km/h passes a railway station platform 250 meters long. What is the total time required for the train to clear the platform?
  22. The speed of a motorboat in still water is 12 km/h and the speed of the river current is 3 km/h. How many hours will the boat take to travel 45 km downstream?
  23. A father is currently four times as old as his son. In 16 years, the father will be twice as old as his son. What is the current age of the father?
  24. The average of five consecutive integers is 27. What is the value of the largest integer in the sequence?
  25. In a training batch of 20 male candidates the average examination score is 60, while for 30 female candidates the average score is 70. What is the combined average score of all 50 candidates?
  26. In what ratio must tea worth 180 BDT per kg be mixed with premium tea worth 240 BDT per kg so that the resulting blended mixture is worth 200 BDT per kg?
  27. What is the smallest positive single-digit integer x such that the five-digit number 56x42 is divisible by 9?
  28. What is the remainder when 2^50 is divided by 7?
  29. Partner A invests 5,000 BDT for a full 12 months in a venture, while Partner B joins with 8,000 BDT for 6 months. In what ratio should the year-end net profit be distributed?
  30. What is the unit digit of the exponential integer 7^95?
  31. Convert the recurring decimal fraction 0.474747... (where 47 repeats infinitely) into a reduced vulgar fraction.
  32. Evaluate the numerical value of the expression: (2/3 + 3/4) / (5/6 - 1/2).
  33. If 35% of a certain number is equal to 140, what is 60% of that same number?
  34. A cash box contains 1-taka, 2-taka, and 5-taka coins in the ratio 4 : 3 : 2, totaling an aggregate value of 200 BDT. How many 5-taka coins are in the box?
  35. What is the greatest four-digit number that is exactly divisible by 12, 15, and 18?

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