2004_Solutions_Grades 3-4-2004_Solutions_Levels

2004_Solutions_Levels_3&4
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This document provides solution suggestions for the Math Kangaroo competition in the USA, specifically for Levels 3 and 4 from the year 2004. Below is a summary of the solutions provided:<br /><br />1. **Question 1**: Calculate a simple sequential sum to find 10,015. Recognize patterns in numbers to simplify calculations.<br /><br />2. **Question 2**: Determine the age difference, which remains constant over time, leads to Mark being 4 years older than his sister.<br /><br />3. **Question 3**: Measure the extra distance added to a path due to a detour, resulting in an additional 6 km.<br /><br />4. **Question 4**: Compare numerical differences to identify the outlier, 278 versus the others at 282.<br /><br />5. **Question 5**: Resolve changes in population of birds based on given movements, concluding with an original count of 14.<br /><br />6. **Question 6**: Use a Venn diagram logic to find numbers in both a rectangle and a circle but not a triangle, resulting in numbers 1 and 10.<br /><br />7. **Question 7**: Apply logic to determine the positioning of red, blue, and green buildings based on given constraints, placing the green building at number 3.<br /><br />8. **Question 8**: Balance shaded versus white squares in a figure by shading 3 additional squares.<br /><br />9. **Question 9**: Identify a visual pattern through rotation, matching figure D after a counterclockwise rotation.<br /><br />10. **Question 10**: Deduce the weight of a pen by using relative weights of pencils and additional masses.<br /><br />11. **Question 11**: Find the correct real time given errors in clock readings, resulting in 5:05 as the true time.<br /><br />12. **Question 12**: Analyze consumption to find that more than half of the fruit remained uneaten.<br /><br />13. **Question 13**: Correct a mistaken operation to find the original number, resulting in 60,000.<br /><br />14. **Question 14**: Subtract known pages to find the total missing sheets, concluding with 10 missing sheets. <br /><br />15. **Question 15**: Use cyclic patterns of days of the week to determine that 52 days after a birthday lands on a Friday.<br /><br />16. **Question 16**: Calculate a column’s sum in a table by algebraically simplifying given equations to arrive at 7.<br /><br />17. **Question 17**: Determine a three-dimensional color arrangement upon folding, resulting in distinct opposite colors.<br /><br />18. **Question 18**: Calculate the side length of a square by manipulating given geometric relations, leading to a length of 64.<br /><br />19. **Question 19**: Count participants given a relative positional clue in a circle, determining a total of 23 students.<br /><br />20. **Question 20**: Conclude that a zero must be included in a digit product of 9 for a 10-digit number, yielding a product of 0.<br /><br />21. **Question 21**: Sum layers of cubes based on alternating colors, reaching a total of 62 white cubes.<br /><br />22. **Question 22**: Distribute a prize money proportionally to contributions, resulting in Peter receiving $375.<br /><br />23. **Question 23**: Analyze soccer game outcomes to identify incompatible results for obtaining 3 points.<br /><br />24. **Question 24**: Solve a grid puzzle using multiplication and distribution of numbers to find specific cells marked by letters, concluding with letters M and S both equaling 12. <br /><br />Each question solved in this document involves mathematical concepts including arithmetic, geometry, logic, and patterns, providing clear insights into problem-solving strategies required for competitive exams.
Keywords
Math Kangaroo
USA
Levels 3 and 4
2004
solutions
arithmetic
geometry
logic
patterns
competitive exams