Difference between revisions of "2007 AMC 8 Problems/Problem 11"

(Created page with '== Problem == Tiles <math>I, II, III</math> and <math>IV</math> are translated so one tile coincides with each of the rectangles <math>A, B, C</math> and <math>D</math>. In the …')
 
(Solution)
Line 14: Line 14:
  
 
<center>[[Image:AMC8_2007_11S.png]]</center>
 
<center>[[Image:AMC8_2007_11S.png]]</center>
 +
 +
==See Also==
 +
{{AMC8 box|year=2007|num-b=10|num-a=12}}

Revision as of 23:37, 12 November 2012

Problem

Tiles $I, II, III$ and $IV$ are translated so one tile coincides with each of the rectangles $A, B, C$ and $D$. In the final arrangement, the two numbers on any side common to two adjacent tiles must be the same. Which of the tiles is translated to Rectangle $C$?

AMC8 2007 11.png

$\mathrm{(A)}\ I \qquad \mathrm{(B)}\ II \qquad \mathrm{(C)}\ III \qquad \mathrm{(D)}\ IV \qquad \mathrm{(E)}$ cannot be determined

Solution

We first notice that tile III has a $0$ on the bottom and a $5$ on the right side. Since no other tile has a $0$ or a $5$, Tile III must be in rectangle $D$. Tile III also has a $1$ on the left, so Tile IV must be in Rectangle $C$.

The answer is $\boxed{D}$

AMC8 2007 11S.png

See Also

2007 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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
Invalid username
Login to AoPS