Question

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 ( $1,000$ meters)?

$9^\text{th}$

$10^\text{th}$

$11^\text{th}$

$12^\text{th}$

$13^\text{th}$

Video solution:

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Written solution:

On the $n$ th jump, the Hulk jumps $2^{n-1}$ meters. We need the smallest $n$ for which $2^{n-1}>1000$ .

Since $2^9=512$ and $2^{10}=1024$ , the first jump longer than $1000$ meters has $n-1=10$ , so $n=11$ .

Thus, C is the correct answer.

2013 AMC 8 Problem 9

Video solution:

Written solution:

Problem 9 in Other Years