2020_Solutions_Grades 11-12-2020_Solutions_Levels

2020_Solutions_Levels_11&12
Pdf Summary
The document provides solution suggestions for the Math Kangaroo 2020 competition, specifically for Level 11-12. Below is a summary of some of the provided solutions:<br /><br />1. **Question 1**: The sum of specific digits is calculated to be 8.<br />2. **Question 2**: The ant’s path is calculated to be 9 meters long through the accumulation of horizontal and vertical segment paths.<br />3. **Question 3**: Approximations and calculations determine that the best representation of a certain product is provided.<br />4. **Question 4**: By managing given percentage categories, it is concluded that 6% of students use a moped.<br />5. **Question 5**: factors contributing to a sum of digits lead to the solution of 24.<br />6. **Question 6**: The original numerical value is manipulated to reveal 7070.<br />7. **Question 7**: Understanding powers led to determining the largest possible value of a variable is 1000.<br />9. **Question 9**: The calculated probability shows that two dice showing the same color is \( \frac{1}{3} \).<br />10. **Question 10**: Through the analysis of multiples, 6 plus one remains non-multiplicative for any integers.<br />11. **Question 11**: Consistency in rectangle area symbolizes a broader understanding.<br />12. **Question 12**: It demonstrates the least steps required to achieve a goal with coins being 3.<br />13. **Question 13**: Spatial reasoning shows that 3 liters of paint suffices given the configuration of boxes.<br />14. **Question 14**: Logical evaluations reject the possibility of a given sum being 1 within constraints.<br />15. **Question 15**: Large calculations demonstrate that 199 digits remain after manipulations.<br />16. **Question 16**: Through an examination of positional equality, the solution concludes that zero is an unreachable total.<br />17. **Question 17**: Geometric relationships within a triangle insist on a solution of 80.<br />18. **Question 18**: Sequence positions analyzed show 673 even numbers among certain total terms.<br />19. **Question 19**: Geometric calculations place value at 72.<br /><br />The document continues with solutions up to problem 30 but illustrates an emphasis on precise mathematical computation, logical deduction, and comprehensive problem analysis throughout the challenge spectrum. Each problem's analysis is directed towards breaking down computations or spatial reasoning within a mathematically logical framework, reflecting the nature of Math Kangaroo problems.
Keywords
Math Kangaroo 2020
Level 11-12
mathematical computation
logical deduction
problem analysis
spatial reasoning
solutions
probability
geometric relationships
sequence positions