2013_Solutions_Grades 7-8-2013_Solutions_Levels

2013_Solutions_Levels_7&8
Pdf Summary
The Math Kangaroo 2013 solution suggestions for Levels 7-8 provide detailed explanations for a series of mathematical problems. Here's a summary of some key solutions:<br /><br />1. <strong>Problem 1</strong>: By dividing the shaded parts of a triangle, the area is calculated to be 6 out of 9 total small triangles.<br /><br />2. <strong>Problem 2</strong>: Solving the given expression results in the answer 55.<br /><br />3. <strong>Problem 3</strong>: Calculating the mass of salt in 1000 kg of sea water results in 35 kg using given equations.<br /><br />4. <strong>Problem 4</strong>: Through visual elimination, 4 is the smallest number of cells remaining after cutting out desired shapes.<br /><br />5. <strong>Problem 5</strong>: The sum of the digits in the smallest two-digit number product of 24 is determined to be 11.<br /><br />6. <strong>Problem 6</strong>: Drawing 6 balls guarantees at least two of the same color.<br /><br />7. <strong>Problem 7</strong>: Considering the burn time of candles, 4 remain lit after 55 minutes.<br /><br />8. <strong>Problem 8</strong>: Calculating realistic averages shows 2.5 cannot be the number of children in five families.<br /><br />9. <strong>Problem 9</strong>: Mark catches up with Liza after 4 circuits due to speed differences.<br /><br />10. <strong>Problem 10</strong>: Solving the equations yields x + y + z = 14.<br /><br />11. <strong>Problem 11</strong>: The diagram shows 8 possible positions for a specific ship layout.<br /><br />12. <strong>Problem 12</strong>: Through angle calculations in a quadrilateral, an angle of 130° is derived.<br /><br />18. <strong>Problem 18</strong>: The analysis reveals 32 cells are not intersected by diagonals in a given grid.<br /><br />23. <strong>Problem 23</strong>: Backtracking from the sum of two numbers reveals the original number's last digit, with the sum of digits being 23.<br /><br />25. <strong>Problem 25</strong>: Based on the race scenario, Andrew finishes ahead of 20 runners.<br /><br />30. <strong>Problem 30</strong>: Analyzing integer properties confirms that all integers satisfying the given condition are divisible by 6.<br /><br />This document serves as guidance for students attempting the Math Kangaroo competition problems, offering logical steps and methodologies for solving each problem.
Keywords
Math Kangaroo 2013
solution suggestions
Levels 7-8
mathematical problems
triangle area
expression solving
mass of salt
visual elimination
digit sum
integer properties