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. **Divisors of Prime Numbers**: The prime numbers that are divisors of 21 include 3 and 7.<br /><br />3. **Clapping Hands**: 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. **Time Calculation**: 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. **Probability with Balls**: 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. **Notebook Distribution**: A charity needs 84 boxes to accommodate all the notebooks, leaving them with 14 extra notebooks.<br /><br />10. **Fruit Basket Purchase**: 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. **Equation Solving with Substitution**: Using provided equations, a solution results in a multiplication leading to a result of 25/8.<br /><br />17. **Language Fluency**: Calculation reveals that 60% of residents speak both English and French, while the rest speak only one language.<br /><br />19. **Geometry Angles**: Various geometry problems conclude with specific angles after deductive reasoning, particularly highlighting the 54-degree angle.<br /><br />27. **Cube Paint Count**: Calculating which cubes in a three-dimensional array are painted on one side leads to identifying 24 specific cubes.<br /><br />30. **Number Sequence**: 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