Difference between revisions of "1993 AJHSME Problems/Problem 13"

(Problem)
(Problem)
Line 11: Line 11:
 
fill((13,3)--(14,3)--(14,4)--(13,4)--cycle,white);
 
fill((13,3)--(14,3)--(14,4)--(13,4)--cycle,white);
 
draw((0,0)--(15,0)--(15,5)--(0,5)--cycle);
 
draw((0,0)--(15,0)--(15,5)--(0,5)--cycle);
label("$5\left\{ \begin{tabular}{c} <br /> <br /> <br /> <br /> \end{tabular}\right.$",(1,2.5),W);
+
 
label(rotate(90)*"$\{$",(0.5,0.1),S);
 
label("$1$",(0.5,-0.6),S);
 
label(rotate(90)*"$\{$",(3.5,0.1),S);
 
label("$1$",(3.5,-0.6),S);
 
label(rotate(90)*"$\{$",(7.5,0.1),S);
 
label("$1$",(7.5,-0.6),S);
 
label(rotate(90)*"$\{$",(11.5,0.1),S);
 
label("$1$",(11.5,-0.6),S);
 
label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(1.5,4),N);
 
label("$3$",(1.5,5.8),N);
 
label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(5.5,4),N);
 
label("$3$",(5.5,5.8),N);
 
label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(9.5,4),N);
 
label("$3$",(9.5,5.8),N);
 
label(rotate(270)*"$\left\{ \begin{tabular}{c} <br /> <br /> \end{tabular}\right.$",(13.5,4),N);
 
label("$3$",(13.5,5.8),N);
 
label("$\left. \begin{tabular}{c} <br /> \end{tabular}\right\} 2$",(14,1),E);
 
 
</asy>
 
</asy>
  

Revision as of 04:55, 25 November 2019

Problem

The word "HELP" in block letters is painted in black with strokes $1$ unit wide on a $5$ by $15$ rectangular white sign with dimensions as shown. The area of the white portion of the sign, in square units, is?

[asy] unitsize(12); fill((0,0)--(0,5)--(1,5)--(1,3)--(2,3)--(2,5)--(3,5)--(3,0)--(2,0)--(2,2)--(1,2)--(1,0)--cycle,black); fill((4,0)--(4,5)--(7,5)--(7,4)--(5,4)--(5,3)--(7,3)--(7,2)--(5,2)--(5,1)--(7,1)--(7,0)--cycle,black); fill((8,0)--(8,5)--(9,5)--(9,1)--(11,1)--(11,0)--cycle,black); fill((12,0)--(12,5)--(15,5)--(15,2)--(13,2)--(13,0)--cycle,black); fill((13,3)--(14,3)--(14,4)--(13,4)--cycle,white); draw((0,0)--(15,0)--(15,5)--(0,5)--cycle);  [/asy]

$\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 34 \qquad \text{(D)}\ 36 \qquad \text{(E)}\ 38$

Solution

Count the number of black squares in each letter. H has 11, E has 11, L has 7, and P has 10, giving the number of black squares to be $11+11+7+10=39$. The total number of squares is $(15)(5)=75$ and the number of white squares is $75-39=\boxed{\text{(D)}\ 36}$.

See Also

1993 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
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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