2005_Solutions_Grades 9-10-2005_Solutions_Levels

2005_Solutions_Levels_9&10
Pdf Summary
This summary contains solutions and explanations for each question in the 2005 Math Kangaroo competition for Levels 9-10. Here is a brief overview of some of the solutions:<br /><br />1. **Eva's Score Position**: Since each student has a different score, and Eva is the 50th best and 50th poorest, there are 99 students total.<br />   <br />2. **Fraction Product**: Multiplying given fractions simplifies to 1/2005. The reciprocal gives the answer, which is 2005.<br /><br />3. **Angle Calculation**: Using properties of angles and triangles, the missing angle is calculated to be 50 degrees.<br /><br />4. **Dimension Increase Impact on Volume**: A 60% increase in one dimension results in a 60% increase in volume.<br /><br />5. **Counting Students in Pairs**: By pairing numbers and adding results, there are 14 boys.<br /><br />6. **Counting Squares and Triangles**: Counting smaller and larger figures results in 3 larger triangles identified.<br /><br />7. **Arranging Strips**: The picture strategy in the exam explains the arrangement solution, resulting in the answer 20.<br /><br />8. **Production Calculation**: The number of components produced, factoring in defect rates, equals 288 non-defective parts.<br /><br />9. **Range of Integer Solutions**: With calculations, numbers like n that fit within given parameters included 2000 to 2004, resulting in 5 integers.<br /><br />10. **Chasing Problem**: For a calculated distance on the track, it took Jumpy’s mother 51 seconds to catch up.<br /><br />11. **Pattern Recognition in Sequence**: A systematic examination of operations result in a final value of 1.<br /><br />12. **Square Area via Integer Sides**: Using integer side lengths, the area calculation result is 121.<br /><br />13. **Rectangle and Circle Area Comparison**: Percentage comparison results in a 48% area for a rectangle compared to a square.<br /><br />14. **Triangle Side Comparison**: Through logical deductions regarding triangles, segment CD is the shortest.<br /><br />15. **Number Ball Pairing**: enough pairs are deduced to get a 10-ball outcome.<br /><br />16. **Juice and Water Mixture Ratio**: Calculating ratios end up with an 11:4 ratio of water to juice.<br /><br />17. **Sum of Triangular Angles**: Using geometric properties, a result of 720 degrees is reached.<br /><br />18. **Prime Factors and Large Divisor**: Detailed factor combination results in 5 four-digit divisors.<br /><br />19. **Solution Omitted**: The problem solutions further continue in original material.<br /><br />These solutions offer structured reasoning and steps to determine correct answers for the questions posed.
Keywords
Math Kangaroo
2005 competition
Level 9-10
Eva's score
fraction product
angle calculation
volume increase
counting students
pattern recognition
prime factors