Psychometric Entrance Test (PET Israel) · Quantitative Reasoning

Algebra, Number Properties and Arithmetic Problem Solving

26 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 26 questions

  1. If n is a positive integer such that 72*n is a perfect cube, what is the smallest possible value of n?
  2. The average of five distinct positive integers is 24. If the median of these five numbers is 20, what is the maximum possible value of the largest of the five numbers?
  3. Pipe A fills a reservoir in 6 hours, and Pipe B fills it in 8 hours. Pipe C drains the full reservoir in 12 hours. If all three pipes are opened simultaneously when the reservoir is empty, how long wi…
  4. In a town, 60% of residents own a bicycle and 40% own a car. If 20% of residents own neither, what percentage of residents own both a bicycle and a car?
  5. A worker's salary was increased by 20%, and one year later reduced by 20%. How does the final salary compare to the original salary?
  6. What is the remainder when 3^100 is divided by 7?
  7. A container holds 60 liters of a mixture of wine and water in the ratio 3:1. How many liters of water must be added so that the ratio of wine to water becomes 1:1?
  8. Three runners start from the same point on a 400-meter circular track, running in the same direction at constant speeds of 4 m/s, 5 m/s, and 8 m/s. After how many seconds will all three runners be tog…
  9. If x, y, and z are positive integers such that x y = 24, y z = 36, and x z = 54, what is the value of x y * z?
  10. The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 45 greater than the original number. What is the original number?
  11. In a sequence of consecutive integers, the sum of the first 7 integers is 70. What is the sum of the next 7 consecutive integers?
  12. If 2^(2x + 1) + 2^(2x - 1) = 40, what is the value of x?
  13. A merchant buys an item for 80 shekels. He marks it up so that after offering a 20% discount on the marked price, he still makes a profit of 25% on his original cost. What was the marked price?
  14. A group of 30 students took an exam where the class average was 78. When the scores of the top 3 students (who averaged 98) and the lowest 2 students (who averaged 48) are removed, what is the average…
  15. If x + y = 7 and x^2 + y^2 = 29, what is the value of (x - y)^2?
  16. Find all real solutions to the equation |2*x - 3| = |x + 6|.
  17. If a and b are the roots of x^2 - 5*x + 3 = 0, what is the value of 1/a^2 + 1/b^2?
  18. For which range of values of k does the quadratic equation x^2 - 2(k - 1)x + (k + 5) = 0 have no real roots?
  19. If 3^(x + y) = 81 and 2^(2x - y) = 32, what is the value of x y?
  20. If 2^(x + 3) - 2^x = 56, what is the value of x?
  21. Solve the rational inequality: (x - 2) / (x + 3) <= 2.
  22. If x + 1/x = 4, what is the value of x^3 + 1/x^3?
  23. Find the value of k such that the system of equations 2x + 3y = 7 and 6x + ky = 20 has no solution.
  24. What is the domain of real values for the function f(x) = sqrt(16 - x^2) / (x - 2)?
  25. If log_2(x) + log_4(x) = 6, what is the value of x?
  26. Find all real solutions to the equation x^4 - 5*x^2 + 4 = 0.

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