2001 AMC 10 Problems
1. The median of the list is 10. What is the mean?
2. A number is more than the product of its reciprocal and its additive inverse. In which interval does the number lie?
3. The sum of two numbers is . Suppose is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?
4. What is the maximum number for the possible points of intersection of a circle and a triangle?
Solutions
1. The median is , therefore . Computation shows that the sum of all numbers is and thus the mean is .
2. The reciprocal of is and the additive inverse is . (Note that must be non-zero to have a reciprocal.) The product of these two is . Thus is more than . Therefore .
3. The original two numbers are and , with . The new two numbers are and . Their sum is .
4. Each side of the triangle can only intersect the circle twice, so the maximum is at most 6. This can be achieved: