Examen Admisión UNMSM (Peru) · Logical-Mathematical Ability

Logical-Mathematical Ability

36 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 36 questions

  1. What is the next term in the series 3, 7, 15, 31, 63, ...?
  2. In a class the ratio of boys to girls is 2 : 3. If there are 45 students in total, how many girls are there?
  3. A shirt costs 500 soles. It is discounted by 20% and then by a further 10% of the reduced price. What is the final price?
  4. Find the next term: 2, 6, 12, 20, 30, ...
  5. A train 120 m long travels at constant speed and passes a pole in 8 seconds. How long does it need to cross a bridge 180 m long, from the front entering to the rear leaving?
  6. Pedro can paint a fence in 12 days and Rosa can paint it in 24 days. Working together at their usual rates, how many days do they need?
  7. The average of five numbers is 18. When one number is removed, the average of the remaining four is 16. What number was removed?
  8. How many different arrangements of the letters of PERU are there if E and U must stay next to each other?
  9. A committee of 3 people is to be chosen from a group of 7 where order does not matter. How many different committees are possible?
  10. Two fair dice are thrown. What is the probability that the sum of the two numbers is 8?
  11. A rectangle has a perimeter of 36 cm and its length is twice its width. What is its area?
  12. A price rises by 25% and then the new price falls by 20%. How does the final price compare with the original?
  13. Ana is taller than Beto, Beto is taller than Carla, and Dina is shorter than Carla. Who is the second tallest?
  14. A father is now four times as old as his son. In 6 years he will be three times as old as his son will be then. How old is the father now?
  15. A 40-litre solution contains 30% alcohol. How many litres of pure alcohol must be added to make a solution that is 50% alcohol?
  16. What is the smaller angle between the hands of a clock at 3:40?
  17. How many diagonals does a convex hexagon have?
  18. What is the sum of the first 20 odd numbers 1, 3, 5, ... ?
  19. Find the next term: 4, 3, 8, 6, 16, 12, ...
  20. What is three quarters of 80?
  21. What simple interest is earned on 2,000 soles at 6% per year over 3 years?
  22. What is the difference between the compound interest and the simple interest earned on 5,000 soles at 10% per year over 2 years?
  23. A car travels 2 hours at 60 km/h and then 1 hour at 90 km/h. What is its average speed for the whole trip?
  24. Two islanders are each either a knight (always truthful) or a knave (always lying). A says: 'At least one of us is a knave.' What are A and B?
  25. Monthly sales in thousands of soles were: January 40, February 55, March 45, April 60. What was the percentage increase from January to February?
  26. A right triangle has legs of 9 cm and 12 cm. How long is the altitude drawn to the hypotenuse?
  27. Using 22/7 for pi, what is the area of a circle of radius 7 cm?
  28. Two lights flash every 12 seconds and every 18 seconds. They flash together at time 0. After how many seconds do they next flash together?
  29. What is the smallest positive number that leaves a remainder of 3 when divided by 5, by 6 and by 8?
  30. How many even three-digit numbers can be formed from the digits 1, 2, 3, 4, 5 if no digit is repeated?
  31. In a group of 60 students, 35 play football, 28 play volleyball and 10 play both. How many play neither sport?
  32. Six workers build a wall in 10 days. Working at the same rate each, how many days would four workers need?
  33. Two numbers add up to 50 and their difference is 14. What is their product?
  34. Fifteen percent of a number is 45. What is the number?
  35. A solid cube of side 4 cm is painted on all faces and then cut into 64 cubes of side 1 cm. How many small cubes have exactly two painted faces?
  36. What is the units digit of 7 raised to the power 2026?

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