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Difference between revisions of "2012 AMC 10B Problems/Problem 20"
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20. Bernardo and Silvia play the following game. An integer between <math>0</math> and <math>999</math>, 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 <math>50</math> to it and passes the result to Bernardo. The winner is the last person who produces a number less than <math>1000</math>. Let <math>N</math> be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of <math>N</math>?
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<math>20.</math> Bernardo and Silvia play the following game. An integer between <math>0</math> and <math>999</math>, 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 <math>50</math> to it and passes the result to Bernardo. The winner is the last person who produces a number less than <math>1000</math>. Let <math>N</math> be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of <math>N</math>?
  
 
<math>(A)</math> <math>7</math>                <math>(B)</math> <math>8</math>                      <math>(C)</math> <math>9</math>                      <math>(D)</math> <math>10</math>                                <math>(E)</math> <math>11</math>
 
<math>(A)</math> <math>7</math>                <math>(B)</math> <math>8</math>                      <math>(C)</math> <math>9</math>                      <math>(D)</math> <math>10</math>                                <math>(E)</math> <math>11</math>

Revision as of 21:00, 28 February 2012

$20.$ 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 $N$?

$(A)$ $7$ $(B)$ $8$ $(C)$ $9$ $(D)$ $10$ $(E)$ $11$

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