2010_Solutions_Grades 7-8-2010_Solutions_Levels

2010_Solutions_Levels_7&8

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The document provides worked solutions to the 30 questions in the 2010 Math Kangaroo USA contest for Grades 7 and 8. The problems cover arithmetic, geometry, number theory, logic, and spatial reasoning. Explanations use strategies such as grouping sums, testing divisibility, working backward, drawing diagrams, applying the Pythagorean theorem, and checking possible answers.

The answer key is: <strong>1 C (404), 2 C (2), 3 D (4), 4 A (6a + 8b), 5 B (square), 6 C (2010), 7 E (30), 8 B (3), 9 B (6), 10 C (100), 11 C (19), 12 D (25), 13 D (45 minutes), 14 B (55), 15 C (19), 16 A, 17 A (1), 18 B (4), 19 E (e), 20 B (1/4), 21 C (64), 22 C (16), 23 E (the altitude’s intersection with side BC), 24 B (5), 25 C (36 cm), 26 C (4 people, 2 liars), 27 B (8), 28 A (11), 29 D (6/7), and 30 D (35).</strong>

Several solutions emphasize recognizing useful patterns: consecutive-number sums, least common multiples, symmetry, area ratios, and constraints in logic or counting problems.

Keywords

Math Kangaroo

contest solutions

Grade 7

Grade 8

arithmetic

geometry

number theory

logic

spatial reasoning

worked solutions