Difference between revisions of "2000 AMC 8 Problems/Problem 9"

m (Problem)
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Three-digit powers of <math>2</math> and <math>5</math> are used in this ''cross-number'' puzzle. What is the only possible digit for the outlined square?
 
Three-digit powers of <math>2</math> and <math>5</math> are used in this ''cross-number'' puzzle. What is the only possible digit for the outlined square?
<cmath>\begin{tabular}{lcl}
+
<cmath>\begin{array}{lcl}
 
\textbf{ACROSS} & & \textbf{DOWN} \\
 
\textbf{ACROSS} & & \textbf{DOWN} \\
 
\textbf{2}. 2^m & & \textbf{1}. 5^n
 
\textbf{2}. 2^m & & \textbf{1}. 5^n
\end{tabular}</cmath>
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\end{array}</cmath>
  
 
<asy>
 
<asy>

Revision as of 19:45, 10 March 2015

Problem

Three-digit powers of $2$ and $5$ are used in this cross-number puzzle. What is the only possible digit for the outlined square? \[\begin{array}{lcl} \textbf{ACROSS} & & \textbf{DOWN} \\ \textbf{2}. 2^m & & \textbf{1}. 5^n \end{array}\]

[asy] draw((0,-1)--(1,-1)--(1,2)--(0,2)--cycle); draw((0,1)--(3,1)--(3,0)--(0,0)); draw((3,0)--(2,0)--(2,1)--(3,1)--cycle,linewidth(1));  label("$1$",(0,2),SE); label("$2$",(0,1),SE); [/asy]

$\text{(A)}\ 0 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8$

Solution

The $3$-digit powers of $5$ are $125$ and $625$, so space $2$ is filled with a $2$. The only $3$-digit power of $2$ beginning with $2$ is $256$, so the outlined block is filled with a $\boxed{\text{(D) 6}}$.

See Also

2000 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
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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