2002_Solutions_Grades 7-8-2002_Solutions_Levels

2002_Solutions_Levels_7&8
Pdf Summary
The Math Kangaroo 2002 solution suggestions provide reasoning and answers for the competition's questions for Levels 7-8. Below is a summary of the solutions for a selection of the problems:<br /><br />1. <strong>Divisors of Prime Numbers</strong>: The prime numbers that are divisors of 21 include 3 and 7.<br /><br />3. <strong>Clapping Hands</strong>: Between numbers 1 and 100, participants clap for numbers that either are multiples of 3 or end with a 3, counting 39 claps in total.<br /><br />4. <strong>Time Calculation</strong>: By dividing the 16 hours and 32 minutes between sunrise and sunset in half, and adding this to the sunrise time, the exact midpoint is calculated as 1:09 P.M.<br /><br />6. <strong>Probability with Balls</strong>: Ada needs to pull at least 12 balls to ensure she gets both white and gray, accounting for a worst-case scenario of drawing only one color repeatedly.<br /><br />7. <strong>Notebook Distribution</strong>: A charity needs 84 boxes to accommodate all the notebooks, leaving them with 14 extra notebooks.<br /><br />10. <strong>Fruit Basket Purchase</strong>: Calculating various combinations, buying 3 kiwi baskets allows the remaining budget to buy exactly one basket of pears and four of oranges.<br /><br />11. <strong>Equation Solving with Substitution</strong>: Using provided equations, a solution results in a multiplication leading to a result of 25/8.<br /><br />17. <strong>Language Fluency</strong>: Calculation reveals that 60% of residents speak both English and French, while the rest speak only one language.<br /><br />19. <strong>Geometry Angles</strong>: Various geometry problems conclude with specific angles after deductive reasoning, particularly highlighting the 54-degree angle.<br /><br />27. <strong>Cube Paint Count</strong>: Calculating which cubes in a three-dimensional array are painted on one side leads to identifying 24 specific cubes.<br /><br />30. <strong>Number Sequence</strong>: Analysis of a sequential number pattern led to recognizing all numbers written were factors of 1000, except those not possible within the given constraints.<br /><br />These solutions illustrate the application of logical reasoning, arithmetic calculations, and geometric principles to solve a range of mathematical problems. Each problem's solution involves breaking down the question, using logical step-by-step reasoning, and arriving at the correct answer.
Keywords
Math Kangaroo 2002
prime numbers
probability
geometry angles
number sequence
logical reasoning
arithmetic calculations
notebook distribution
language fluency
cube paint count