1998_Solutions_Grades 7-8-1998_Solutions_Levels

1998_Solutions_Levels_7&8
Pdf Summary
The Math Kangaroo 1998 solution suggestions provide explanations for contest questions aimed at levels 7 and 8. Each solution is detailed with an answer and the logical or mathematical reasoning behind it. Here's a summary of the provided solutions:<br /><br />1. **KANGOUROU Puzzle (Q1):** Using as few as three pieces can construct the word.<br />2. **Area Comparison (Q2):** Only shapes 1 and 5 have the same area.<br />3. **Number Game (Q3):** The smallest possible number sequence formed by alternating choices is 254361.<br />4. **Geometry Problem (Q4):** The segment connecting midpoints in a triangle is 2 cm.<br />5. **Word Mirror Image (Q5):** No specific image provided.<br />6. **Circle Division (Q6):** John can only perform two divisions.<br />7. **Finding Angles (Q7):** By understanding relationships and using provided angles, missing angles are determined.<br />8. **Calendar Puzzle (Q8):** Only with a 31-day month could January have 4 Mondays and 4 Fridays, starting on a Tuesday.<br />9. **House Image Difference (Q9):** Image differs in picture B.<br />10. **Hexagon and Triangles (Q10):** The area of the hexagon is calculated to be 24.<br />11. **Juice Sugar Content (Q11):** Combining two different sugar percentages results in 13%.<br />12. **Triangle Bisectors (Q12):** Relationships in bisectors lead to an angle measure of 120°.<br />13. **Combinations of Groups (Q13):** Eight combinations of non-married groups can be made.<br />14. **Triangle and Hexagon Ratio (Q14):** The area ratio is shown to be 1/3.<br />15. **Prime Product Ending (Q15):** The last digit in a product involving prime numbers less than 1998 is 0.<br />16. **Percentage of Boys (Q16):** From the context given, the percentage is 125%.<br />17. **Radius Calculation (Q17):** The radius of a smaller circle is 15.<br />18. **Inequality Error (Q18):** Mistake identified between steps 4 and 5 due to inequalities and number handling.<br />19. **Chairs and Stools (Q19):** Correct setup includes 3 stools and 4 chairs.<br />20. **Angle Calculation (Q20):** Green angles in a geometry set equal 40°.<br />21. **Lacing Pattern (Q21):** Proper pattern cannot be obtained from B.<br />22. **Palindrome Numbers (Q22):** There are 1000 possible 6-digit palindromes.<br />23. **Block Set in a Box (Q23):** Total blocks fitting into the box are 64.<br />24. **Triangles and Diagonals (Q24):** Quadilateral diagonal length determined as 2.8.<br />25. **Median Areas (Q25):** Multiple equal-sized triangles within, totaling an area of 7.<br />26. **Impossible Configuration (Q26):** With 18 lines, task cannot be performed.<br />27. **Elements Chosen from Set (Q27):** Largest set where sums are not divisible by 3 has 10 elements.<br />28. **Soap Bar Usage (Q28):** 8 more days until the soap bar is used up.<br />29. **Number Elimination (Q29):** Through successive eliminations, 1024 is remaining.<br />30. **Equation Solution (Q30):** Satisfies condition when x - y = 7.<br /><br />These solutions illustrate the diverse math topics and concepts covered in the Math Kangaroo competition, including geometry, algebra, number theory, and pattern recognition. Each problem demands careful consideration to apply mathematical principles effectively.
Keywords
Math Kangaroo 1998
contest solutions
geometry problems
algebra concepts
number theory
pattern recognition
mathematical reasoning
problem-solving
logic puzzles
area calculations