2013 AMC 8 Problems/Problem 9
Problem
The Incredible Hulk can double the distance he jumps with each succeeding jump. If his first jump is 1 meter, the second jump is 2 meters, the third jump is 4 meters, and so on, then on which jump will he first be able to jump more than 1 kilometer?
Solution
This is a geometric sequence in which the common ratio is 2. To find the jump that would be over a 1000 meters, we note that .
However, because the first term is and not , the solution to the problem is
Solution 2
We can also solve this problem by listing out how far the Hulk jumps on each jump: on the first jump, he goes 1 meter, the second jump 2 meters, and so on. Listing out these numbers, we get:
On the 11th jump, the Hulk jumps 1024 meters > 1000 meters (1 kilometer), so our answer is the 11th jump, or
Solution 3
The smallest power of two that is larger or equal to 1000 is , or Thus, the answer is
See Also
2013 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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