University of Bahrain Aptitude Test (UOB Aptitude) · Mathematics Reasoning

Quantitative Reasoning and Algebra

31 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 31 questions

  1. Solve for x in the linear equation: 3(2x - 5) - 4(x + 2) = 7.
  2. If a store increases the price of an electronic device by 20% and later discounts the new price by 25%, what is the overall percentage change from the initial price?
  3. Find the solution set for the absolute value inequality: |2x - 7| <= 9.
  4. Solve the quadratic equation for real roots: 2x^2 - 5x - 12 = 0.
  5. If 5 workers can build a wall in 12 days, how many days will 6 workers take to build the identical wall working at the same pace?
  6. Simplify the algebraic rational expression: (x^2 - 16) / (x^2 + 7x + 12).
  7. Find the 15th term of an arithmetic progression whose first term is 4 and common difference is 3.
  8. A chemist mixes 20 liters of a 30% acid solution with 30 liters of a 50% acid solution. What is the acid percentage of the resulting mixture?
  9. Solve the system of linear equations for x and y: 3x + 2y = 16 and 2x - y = 6. What is the value of x + y?
  10. Simplify the exponential expression: (2^5 * 8^2) / 4^4.
  11. In how many distinct ways can a committee of 3 students be chosen from a group of 8 eligible candidates?
  12. Find the sum of the first 8 terms of the geometric series: 3, 6, 12, 24, ...
  13. A car travels 180 km at an average speed of 60 km/h and returns along the same route at 90 km/h. What is the average speed of the car for the entire round trip?
  14. Solve the linear inequality for x: 5 - 2(3x - 1) > 4x - 13.
  15. If x^2 + y^2 = 50 and xy = 7, find the positive value of x + y.
  16. Factor completely the polynomial: 3x^3 - 12x.
  17. A bank deposit of 5,000 BHD earns 6% annual simple interest. How much total interest is earned after 4 years?
  18. Find the domain of the real-valued function: f(x) = sqrt(3x - 15).
  19. If log_2(x) + log_2(x - 3) = 2, find the valid real solution for x.
  20. The perimeter of a rectangle is 48 cm and its length is 6 cm longer than its width. What is the area of the rectangle?
  21. Simplify the radical expression: sqrt(75) - sqrt(27) + sqrt(12).
  22. If a polygon has 9 sides (a nonagon), what is the sum of its interior angles?
  23. Find the value of k such that the polynomial P(x) = 2x^3 - kx^2 + 3x - 2 is exactly divisible by (x - 2).
  24. A pipe fills an empty reservoir in 6 hours, while a drainage pipe empties it in 10 hours. If both pipes are opened simultaneously, how long does it take to fill the reservoir?
  25. Find the sum of the infinite geometric series: 12 + 4 + 4/3 + 4/9 + ...
  26. If 3^(2x - 1) = 27^(x - 2), find the value of x.
  27. A retailer purchases 50 shirts at $20 each. He sells 30 of them at a 30% profit and the remaining 20 shirts at a 10% loss. What is his overall net percentage profit on the entire batch?
  28. Three pipes X, Y, and Z can fill a cistern in 10, 15, and 30 hours respectively. If all three pipes are opened together, how many hours will it take to fill the cistern completely?
  29. If and , what is the value of ?
  30. A car travels the first half of a distance at 60 km/h and the second half at 90 km/h. What is the average speed of the car for the entire journey?
  31. The perimeter of a right-angled triangle is 60 cm, and its hypotenuse is 25 cm. What is the area of the triangle?

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