2012 AMC 10B Problems/Problem 20

Problem

Bernardo and Silvia play the following game. An integer between $0$ and $999$ , inclusive, is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she adds $50$ to it and passes the result to Bernardo. The winner is the last person who produces a number less than $1000$ . Let $N$ be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of $N$ ?

$\textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 11$

Solution

Let's test each solution, for our first case $7$ , we start out with $7$ and the number is then given to Bernardo. He will double the given number so in this case $7\times 2\equals 14$ (Error compiling LaTeX. Unknown error_msg)

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2012 AMC 10B Problems/Problem 20

Problem

Solution