Psychometric Entrance Test (PET Israel) · Quantitative Reasoning

Plane Geometry, Coordinate Systems and Data Interpretation

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. In a right triangle ABC with hypotenuse AC = 10, angle BAC = 30 degrees. What is the area of triangle ABC?
  2. A circle of radius r is inscribed in an equilateral triangle of side length 12. What is the area of the circle?
  3. A square is inscribed in a right isosceles triangle such that one side of the square lies on the hypotenuse. If the hypotenuse has length 12, what is the side length of the square?
  4. A sector of a circle with central angle 120 degrees has an arc length of 8*pi cm. What is the area of the sector?
  5. In triangle ABC, side AB = 7, side BC = 8, and angle ABC = 60 degrees. What is the length of side AC?
  6. A regular hexagon has perimeter 36 cm. What is its total area?
  7. Two chords AB and CD intersect inside a circle at point P. If AP = 4, PB = 9, and CP = 3, what is the length of chord CD?
  8. A right circular cone has base radius 6 cm and slant height 10 cm. What is its total surface area (including base)?
  9. In trapezoid ABCD with parallel bases AB and CD, AB = 6 and CD = 14. The diagonals intersect at point E. If the area of triangle ABE is 18, what is the area of trapezoid ABCD?
  10. What is the volume of a sphere inscribed inside a cube of side length 6?
  11. A cylindrical tank of radius 4 m and height 10 m is filled with water to a depth of 6 m. How many cubic meters of water are in the tank?
  12. Points A, B, and C lie on a circle centered at O. If angle AOC = 100 degrees, what is the measure of the inscribed angle ABC subtending the major arc AC?
  13. A rectangle has perimeter 28 and diagonal 10. What is the area of the rectangle?
  14. Three mutually tangent circles of radius 1 are placed on a flat plane. A rubber band is stretched tightly around all three circles. What is the total length of the rubber band?
  15. How many distinct 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 if no digit may be repeated?
  16. A committee of 4 people is to be selected from a group of 6 men and 5 women. What is the probability that the committee contains exactly 2 men and 2 women?
  17. Two fair 6-sided dice are rolled simultaneously. What is the probability that the sum of the numbers rolled is a prime number?
  18. In how many ways can 5 boys and 5 girls sit in a row such that all boys sit together and all girls sit together?
  19. A bag contains 5 red balls and 7 blue balls. Two balls are drawn successively without replacement. What is the probability that both balls are of different colors?
  20. How many integer solutions (x_1, x_2, x_3) satisfy x_1 + x_2 + x_3 = 12, where x_1 >= 1, x_2 >= 1, and x_3 >= 1?
  21. A company has 100 employees. 70 speak English, 45 speak French, and 10 speak neither. If an employee is chosen at random and is known to speak English, what is the probability that they also speak Fre…
  22. In a factory producing light bulbs, Machine A produces 60% of the bulbs with a 2% defect rate, while Machine B produces 40% of the bulbs with a 5% defect rate. If a randomly selected bulb is found to…
  23. A code consists of 3 distinct letters followed by 2 distinct digits. How many such codes can be formed from the 26 English letters and the 10 digits (0-9)?
  24. The median of a set of 9 distinct integers is 40. If each integer in the set is multiplied by 3 and then increased by 5, what is the median of the new set?
  25. A box contains 4 red balls, 3 green balls, and 2 yellow balls. If 3 balls are drawn at random without replacement, what is the probability that all 3 balls have different colors?
  26. In a survey of 120 tourists, 75 visited Jerusalem, 60 visited Tel Aviv, and 45 visited Haifa. Exactly 30 visited both Jerusalem and Tel Aviv, 25 visited both Jerusalem and Haifa, and 20 visited both T…

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