FUVEST (University of São Paulo Entrance Exam) · Mathematics and Physics

Mathematics: Equations and Problem Solving

12 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 12 questions

  1. Two numbers add up to 7 and their difference is 5. What is the larger number?
  2. Pipe A fills a tank in 6 hours and pipe B fills it in 3 hours. Working together, how many hours do they need?
  3. Pipe A fills a tank in 15 hours and pipe B fills it in 10 hours. Working together, how many hours do they need?
  4. Pipe A fills a tank in 20 hours and pipe B fills it in 5 hours. Working together, how many hours do they need?
  5. What is the sum of the solutions of |x - 8| = 8?
  6. 3 pens and 1 notebook cost $31; 1 pen and 2 notebooks cost $17. What is the price of one pen?
  7. Ana is 2 times as old as Bia. In 5 years the sum of their ages will be 43. How old is Bia now?
  8. Pipe A fills a tank in 12 hours and pipe B fills it in 6 hours. Working together, how many hours do they need?
  9. Solve the equation .
  10. A rectangle has a perimeter of 30 cm, and its length is twice its width. What is its area?
  11. The product of two consecutive positive integers is 132. What is their sum?
  12. A cinema sold 200 tickets, some at the full price of 30 reais and the rest at the half price of 15 reais, taking 4,800 reais in total. How many half-price tickets were sold?

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