Difference between revisions of "2000 AMC 8 Problems/Problem 9"
Mathgeek2006 (talk | contribs) m (→Problem) |
m (minor edit) |
||
Line 1: | Line 1: | ||
− | ==Problem== | + | == Problem == |
− | |||
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{array}{lcl} | <cmath>\begin{array}{lcl} | ||
Line 18: | Line 17: | ||
<math>\text{(A)}\ 0 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math> | <math>\text{(A)}\ 0 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math> | ||
− | ==Solution== | + | == Solution == |
− | |||
The <math>3</math>-digit powers of <math>5</math> are <math>125</math> and <math>625</math>, so space <math>2</math> is filled with a <math>2</math>. | The <math>3</math>-digit powers of <math>5</math> are <math>125</math> and <math>625</math>, so space <math>2</math> is filled with a <math>2</math>. | ||
The only <math>3</math>-digit power of <math>2</math> beginning with <math>2</math> is <math>256</math>, so the outlined block is filled with | The only <math>3</math>-digit power of <math>2</math> beginning with <math>2</math> is <math>256</math>, so the outlined block is filled with | ||
a <math>\boxed{\text{(D) 6}}</math>. | a <math>\boxed{\text{(D) 6}}</math>. | ||
− | ==See Also== | + | == See Also == |
− | |||
{{AMC8 box|year=2000|num-b=8|num-a=10}} | {{AMC8 box|year=2000|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 12:30, 19 October 2020
Problem
Three-digit powers of and are used in this cross-number puzzle. What is the only possible digit for the outlined square?
Solution
The -digit powers of are and , so space is filled with a . The only -digit power of beginning with is , so the outlined block is filled with a .
See Also
2000 AMC 8 (Problems • Answer Key • Resources) | ||
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.