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Difference between revisions of "2005 AMC 8 Problems/Problem 24"

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First we can start at 200 and work our way down we want to do /2 the most so if we come across an odd number we just subtract 1! So <math>200/2</math>=100, 100/2=50, 50/2=25, 25-1=24, 24/2=12, 12/2=6, 6/2=3, 3-1=2, and 2/2=1. We made our way back to 1 but since it is the amount of times the button is pressed than the answer should be \boxed{\textbf{(B)}\ 9}$.
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First we can start at 200 and work our way down we want to do <math>/2</math> the most so if we come across an odd number we just subtract 1. So <math>200/2</math>=<math>100</math>, <math>100/2</math>=<math>50</math>, <math>50/2</math>=<math>25</math>, <math>25-1</math>=<math>24</math>, <math>24/2</math>=12<math>, </math>12/2<math>=</math>6<math>, </math>6/2<math>=</math>3<math>, </math>3-1<math>=</math>2<math>, and </math>2/2<math>=</math>1<math>. We made our way back to 1 but since it is the amount of times the button is pressed than the answer should be \boxed{\textbf{(B)}\ 9}</math>.
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2005|num-b=23|num-a=25}}
 
{{AMC8 box|year=2005|num-b=23|num-a=25}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 14:31, 28 September 2020

Problem

A certain calculator has only two keys [+1] and [x2]. When you press one of the keys, the calculator automatically displays the result. For instance, if the calculator originally displayed "9" and you pressed [+1], it would display "10." If you then pressed [x2], it would display "20." Starting with the display "1," what is the fewest number of keystrokes you would need to reach "200"?

$\textbf{(A)}\ 8\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 11\qquad\textbf{(E)}\ 12$

Solution

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First we can start at 200 and work our way down we want to do $/2$ the most so if we come across an odd number we just subtract 1. So $200/2$=$100$, $100/2$=$50$, $50/2$=$25$, $25-1$=$24$, $24/2$=12$,$12/2$=$6$,$6/2$=$3$,$3-1$=$2$, and$2/2$=$1$. We made our way back to 1 but since it is the amount of times the button is pressed than the answer should be \boxed{\textbf{(B)}\ 9}$.

See Also

2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 23 		Followed by
Problem 25
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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