2013_Solutions_Grades 7-8-2013_Solutions_Levels

2013_Solutions_Levels_7&8

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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. **Problem 1**: By dividing the shaded parts of a triangle, the area is calculated to be 6 out of 9 total small triangles.<br /><br />2. **Problem 2**: Solving the given expression results in the answer 55.<br /><br />3. **Problem 3**: Calculating the mass of salt in 1000 kg of sea water results in 35 kg using given equations.<br /><br />4. **Problem 4**: Through visual elimination, 4 is the smallest number of cells remaining after cutting out desired shapes.<br /><br />5. **Problem 5**: The sum of the digits in the smallest two-digit number product of 24 is determined to be 11.<br /><br />6. **Problem 6**: Drawing 6 balls guarantees at least two of the same color.<br /><br />7. **Problem 7**: Considering the burn time of candles, 4 remain lit after 55 minutes.<br /><br />8. **Problem 8**: Calculating realistic averages shows 2.5 cannot be the number of children in five families.<br /><br />9. **Problem 9**: Mark catches up with Liza after 4 circuits due to speed differences.<br /><br />10. **Problem 10**: Solving the equations yields x + y + z = 14.<br /><br />11. **Problem 11**: The diagram shows 8 possible positions for a specific ship layout.<br /><br />12. **Problem 12**: Through angle calculations in a quadrilateral, an angle of 130° is derived.<br /><br />18. **Problem 18**: The analysis reveals 32 cells are not intersected by diagonals in a given grid.<br /><br />23. **Problem 23**: Backtracking from the sum of two numbers reveals the original number's last digit, with the sum of digits being 23.<br /><br />25. **Problem 25**: Based on the race scenario, Andrew finishes ahead of 20 runners.<br /><br />30. **Problem 30**: 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