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

(Created page with "==Problem== The word "'''HELP'''" in block letters is painted in black with strokes <math>1</math> unit wide on a <math>5</math> by <math>15</math> rectangular white sign with d...")
 
(→‎Problem)
 
(4 intermediate revisions by 4 users not shown)
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("$5\left\{ \begin{tabular}{c} \\ \\ \\ \\ \end{tabular}\right.$",(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)*"$\left\{ \begin{tabular}{c} \\ \\ \end{tabular}\right.$",(1.5,4),N);
 
−
label("$3$",(1.5,5.8),N);
 
−
label(rotate(270)*"$\left\{ \begin{tabular}{c} \\ \\ \end{tabular}\right.$",(5.5,4),N);
 
−
label("$3$",(5.5,5.8),N);
 
−
label(rotate(270)*"$\left\{ \begin{tabular}{c} \\ \\ \end{tabular}\right.$",(9.5,4),N);
 
−
label("$3$",(9.5,5.8),N);
 
−
label(rotate(270)*"$\left\{ \begin{tabular}{c} \\ \\ \end{tabular}\right.$",(13.5,4),N);
 
−
label("$3$",(13.5,5.8),N);
 
−
label("$\left. \begin{tabular}{c} \\ \end{tabular}\right\} 2$",(14,1),E);
 
 
</asy>
 
</asy>
  
 
<math>\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 34 \qquad \text{(D)}\ 36 \qquad \text{(E)}\ 38</math>
 
<math>\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 34 \qquad \text{(D)}\ 36 \qquad \text{(E)}\ 38</math>
 +
 +
==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 <math>11+11+7+10=39</math>. The total number of squares is <math>(15)(5)=75</math> and the number of white squares is <math>75-39=\boxed{\text{(D)}\ 36}</math>.
 +
 +
==See Also==
 +
{{AJHSME box|year=1993|num-b=12|num-a=14}}
 +
{{MAA Notice}}

Latest revision as of 03:55, 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 (Problems • Answer Key • Resources)
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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