2012_Solutions_Grades 5-6-2012_Solutions_Levels

2012_Solutions_Levels_5&6
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The document details the solutions and answers to the Math Kangaroo 2012 competition, held in the USA. Each question is numbered and followed by a brief explanation or calculation which leads to the correct answer choice. It includes various types of mathematical problems such as geometry, algebra, number theory, and logical puzzles.<br /><br />1. The solution explains that Basil needs 9 different colors for the 9 unique letters in "VIVAT KANGAROO."<br />2. The width of the blackboard's right-hand part is calculated to be 1.5 m by dividing the remaining width (after subtracting the middle part) equally.<br />3. To enclose 16 non-overlapping coins in a square, Sally needs 8 matches based on geometric arrangement.<br />4. The total number of passenger seats is calculated by summing the configurations of different rows, resulting in 142 seats.<br />5. By considering the time zones and working backward from when Ann went to bed, the time in Madrid is calculated to be 6 o'clock that morning.<br />6. The answer involves understanding geometric shapes in a hexagonal arrangement, leading to the construction of a larger equilateral triangle.<br />7. The arithmetic steps are broken down to find the result of the expression, which is calculated as 7.<br />8. Rotational symmetry is used to determine the position of figures on coins to match the specified arrangement.<br />9. Calculations show that a balloon can cover the weight of the basket, plusing an additional load, revealing the basket's weight.<br />10. The number of pears and apples consumed and their original numbers are analyzed to find the total.<br />11. Jigsaw-like logic is used to fit puzzle pieces into a coherent arrangement, satisfying specific boundary conditions.<br />12. By exclusion based on visible sides, a die is determined to have letter B.<br />13. Combines and calculates potential pairings to reveal the number of non-visible roads.<br />14. Explores color classification of products from multiples of numbers.<br />15. Using perimeter and area measurements, the size of a geometric shape is calculated.<br />16. Perimeter differences are analyzed between curved and line segments of circles.<br />17. An analysis of sum and average concepts helps verify a puzzle involving several numbers.<br />18. Describes consecutive bouncing and height differences of a ball until it stops surpassing a window's position.<br />19. Counts revolutions of a series of interconnected gears with respect to each other.<br />20. Understands symmetry in cutting and folding paper to reveal geometric patterns.<br />21. Quantitative comparisons of liquids are interpreted with basic arithmetic.<br />22. Describes the path taken through a number system on stones.<br />23. Calculations to find the average involve understanding age distribution and attendance.<br />24. Analysis of perimeter measurements in rectangles involves combination logic.<br />25. Logical trial and error is used to define neighboring numbers in a sequence.<br />26. Describes the minimum use of squares to tile a larger rectangular space.<br />27. Logic and color-coding reasoning through elimination led to the correct grid configuration.<br />28. Folding and geometry comprehension help find the area of certain regions within a shape.<br />29. Algebraic manipulation determines the sequence of digits in a house number problem.<br />30. Logical deduction disallows certain options to arrive at a numeric code for a given condition.<br /><br />Throughout the document, the solutions rely on mathematical concepts such as arithmetic calculations, geometric reasoning, logic puzzles, and alternative explanations, while also occasionally providing visual clues or hypothetical scenarios for clarity.
Keywords
Math Kangaroo 2012
geometry
algebra
number theory
logical puzzles
USA competition
solutions
calculations
mathematical problems
explanations