Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2012 AMC 10B Problems/Problem 20"

(Created page with "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 ...")
 
Line 1: Line 1:
 
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>?
 
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>?
  
−
<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 20:58, 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 $N$?

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2012_AMC_10B_Problems/Problem_20&oldid=45213"