Difference between revisions of "2003 AMC 8 Problems"

(Problem 16)
(Problem 10)
 
(42 intermediate revisions by 13 users not shown)
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==Problem 3==
 
==Problem 3==
A burger at Ricky C's weighs <math>120</math> grams, of which <math>30</math> grams are filler.  
+
A burger at Ricky C's weighs 120 grams, of which 30 grams are filler. What percent of the burger is not filler?
What percent of the burger is not filler?
 
  
 
<math>\mathrm{(A)}\ 60\% \qquad\mathrm{(B)}\ 65\% \qquad\mathrm{(C)}\ 70\% \qquad\mathrm{(D)}\ 75\% \qquad\mathrm{(E)}\ 90\%</math>
 
<math>\mathrm{(A)}\ 60\% \qquad\mathrm{(B)}\ 65\% \qquad\mathrm{(C)}\ 70\% \qquad\mathrm{(D)}\ 75\% \qquad\mathrm{(E)}\ 90\%</math>
Line 22: Line 21:
  
 
==Problem 4==
 
==Problem 4==
A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted <math>7</math> children and <math>19</math> wheels. How many tricycles were there?
+
A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted 7 children and 19 wheels. How many tricycles were there?
  
 
<math>\mathrm{(A)}\ 2 \qquad\mathrm{(B)}\ 4 \qquad\mathrm{(C)}\ 5 \qquad\mathrm{(D)}\ 6 \qquad\mathrm{(E)}\ 7</math>
 
<math>\mathrm{(A)}\ 2 \qquad\mathrm{(B)}\ 4 \qquad\mathrm{(C)}\ 5 \qquad\mathrm{(D)}\ 6 \qquad\mathrm{(E)}\ 7</math>
Line 29: Line 28:
  
 
==Problem 5==
 
==Problem 5==
If <math> 20\% </math> of a number is <math>12</math>, what is <math> 30\% </math> of the same number?
+
If 20% of a number is 12, what is 30% of the same number?
  
 
<math>\mathrm{(A)}\ 15\qquad\mathrm{(B)}\ 18 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 24 \qquad\mathrm{(E)}\ 30</math>
 
<math>\mathrm{(A)}\ 15\qquad\mathrm{(B)}\ 18 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 24 \qquad\mathrm{(E)}\ 30</math>
  
[[2005 AMC 8 Problems/Problem 5|Solution]]
+
[[2003 AMC 8 Problems/Problem 5|Solution]]
  
 
==Problem 6==
 
==Problem 6==
Given the areas of the three squares in the figure, what is the area of the interior triangle? [[File:AMC8 problem 6 2003image.png]]
+
Given the areas of the three squares in the figure, what is the area of the interior triangle?
 +
 
 +
<asy>
 +
draw((0,0)--(-5,12)--(7,17)--(12,5)--(17,5)--(17,0)--(12,0)--(12,-12)--(0,-12)--(0,0)--(12,5)--(12,0)--cycle,linewidth(1));
 +
label("$25$",(14.5,1),N);
 +
label("$144$",(6,-7.5),N);
 +
label("$169$",(3.5,7),N);
 +
</asy>
  
 
<math>\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 30 \qquad\mathrm{(C)}\ 60 \qquad\mathrm{(D)}\ 300 \qquad\mathrm{(E)}\ 1800</math>
 
<math>\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 30 \qquad\mathrm{(C)}\ 60 \qquad\mathrm{(D)}\ 300 \qquad\mathrm{(E)}\ 1800</math>
Line 43: Line 49:
  
 
==Problem 7==
 
==Problem 7==
Blake and Jenny each took four <math>100</math>-point tests. Blake averaged <math>78</math> on the four tests. Jenny scored <math>10</math> points higher than Blake on the first test, <math>10</math> points lower than him on the second test, and <math>20</math> points higher on both the third and fourth tests. What is the difference between Jenny's average and Blake's average on these four tests?
+
Blake and Jenny each took four 100-point tests. Blake averaged 78 on the four tests. Jenny scored 10 points higher than Blake on the first test, 10 points lower than him on the second test, and 20 points higher on both the third and fourth tests. What is the difference between Jenny's average and Blake's average on these four tests?
  
 
<math> \mathrm{(A)}\  10  \qquad\mathrm{(B)}\ 15 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 25 \qquad\mathrm{(E)}\ 40 </math>
 
<math> \mathrm{(A)}\  10  \qquad\mathrm{(B)}\ 15 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 25 \qquad\mathrm{(E)}\ 40 </math>
Line 49: Line 55:
 
[[2003 AMC 8 Problems/Problem 7|Solution]]
 
[[2003 AMC 8 Problems/Problem 7|Solution]]
  
==Bake Sale==
+
==Problem 8==
Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures
+
<math>\textbf{Bake Sale}</math>
 +
 
 +
(Problems 8, 9, and 10 use the data found in the accompanying paragraph and figures)
  
 
Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
 
Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
  
<math>\circ</math> Art's cookies are trapezoids:
+
<math>\circ</math> Art's cookies are trapezoids.
<asy>size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
+
<asy>
 +
size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
 
draw(origin--(5,0)--(5,3)--(2,3)--cycle);
 
draw(origin--(5,0)--(5,3)--(2,3)--cycle);
 
draw(rightanglemark((5,3), (5,0), origin));
 
draw(rightanglemark((5,3), (5,0), origin));
 
label("5 in", (2.5,0), S);
 
label("5 in", (2.5,0), S);
 
label("3 in", (5,1.5), E);
 
label("3 in", (5,1.5), E);
label("3 in", (3.5,3), N);</asy>
+
label("3 in", (3.5,3), N);
 +
</asy>
  
<math>\circ</math> Roger's cookies are rectangles:
+
<math>\circ</math> Roger's cookies are rectangles.
<asy>size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
+
<asy>
 +
size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
 
draw(origin--(4,0)--(4,2)--(0,2)--cycle);
 
draw(origin--(4,0)--(4,2)--(0,2)--cycle);
 
draw(rightanglemark((4,2), (4,0), origin));
 
draw(rightanglemark((4,2), (4,0), origin));
 
draw(rightanglemark((0,2), origin, (4,0)));
 
draw(rightanglemark((0,2), origin, (4,0)));
 
label("4 in", (2,0), S);
 
label("4 in", (2,0), S);
label("2 in", (4,1), E);</asy>
+
label("2 in", (4,1), E);
 +
</asy>
  
<math>\circ</math> Paul's cookies are parallelograms:
+
<math>\circ</math> Paul's cookies are parallelograms.
<asy>size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
+
<asy>
 +
size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
 
draw(origin--(3,0)--(2.5,2)--(-0.5,2)--cycle);
 
draw(origin--(3,0)--(2.5,2)--(-0.5,2)--cycle);
 
draw((2.5,2)--(2.5,0), dashed);
 
draw((2.5,2)--(2.5,0), dashed);
 
draw(rightanglemark((2.5,2),(2.5,0), origin));
 
draw(rightanglemark((2.5,2),(2.5,0), origin));
 
label("3 in", (1.5,0), S);
 
label("3 in", (1.5,0), S);
label("2 in", (2.5,1), W);</asy>
+
label("2 in", (2.5,1), W);
 +
</asy>
  
<math>\circ</math> Trisha's cookies are triangles:
+
<math>\circ</math> Trisha's cookies are triangles.
<asy>size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
+
<asy>
 +
size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
 
draw(origin--(3,0)--(3,4)--cycle);
 
draw(origin--(3,0)--(3,4)--cycle);
 
draw(rightanglemark((3,4),(3,0), origin));
 
draw(rightanglemark((3,4),(3,0), origin));
 
label("3 in", (1.5,0), S);
 
label("3 in", (1.5,0), S);
label("4 in", (3,2), E);</asy>
+
label("4 in", (3,2), E);
 +
</asy>
  
==Problem 8==
+
Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Who gets the fewest cookies from one batch of cookie dough?
Who gets the fewest cookies from one batch of cookie dough?
 
  
<math> \textbf{(A)}\ \text{Art} \qquad\textbf{(B)}\ \text{Paul}\qquad\textbf{(C)}\ \text{Roger}\qquad\textbf{(D)}\ \text{Trisha}\qquad\textbf{(E)}\ \text{There is a tie for fewest}</math>
+
<math> \textbf{(A)}\ \text{Art}\qquad\textbf{(B)}\ \text{Roger}\qquad\textbf{(C)}\ \text{Paul}\qquad\textbf{(D)}\ \text{Trisha}\qquad\textbf{(E)}\ \text{There is a tie for fewest.} </math>
  
 
[[2003 AMC 8 Problems/Problem 8|Solution]]
 
[[2003 AMC 8 Problems/Problem 8|Solution]]
Line 107: Line 122:
  
 
==Problem 11==
 
==Problem 11==
Business is a little slow at Lou's Fine Shoes, so Lou decides to have a
+
 
sale. On Friday, Lou increases all of Thursday's prices by <math> 10% </math>. Over the
+
Business is a little slow at Lou's Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday's prices by 10%. Over the weekend, Lou advertises the sale: "Ten percent off the listed price. Sale starts Monday." How much does a pair of shoes cost on Monday that cost 40 dollars on Thursday?
weekend, Lou advertises the sale: Ten percent off the listed price. Sale
 
starts Monday." How much does a pair of shoes cost on Monday that
 
cost <math> 40 </math> dollars on Thursday?
 
  
 
<math> \textbf{(A)}\ 36\qquad\textbf{(B)}\ 39.60\qquad\textbf{(C)}\ 40\qquad\textbf{(D)}\ 40.40\qquad\textbf{(E)}\ 44 </math>
 
<math> \textbf{(A)}\ 36\qquad\textbf{(B)}\ 39.60\qquad\textbf{(C)}\ 40\qquad\textbf{(D)}\ 40.40\qquad\textbf{(E)}\ 44 </math>
Line 118: Line 130:
  
 
==Problem 12==
 
==Problem 12==
When a fair six-sided die is tossed on a table top, the bottom face cannot
+
 
be seen. What is the probability that the product of the numbers on the
+
When a fair six-sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the numbers on the five faces that can be seen is divisible by 6?
five faces that can be seen is divisible by 6?
 
  
 
<math> \textbf{(A)}\ \frac{1}{3}\qquad\textbf{(B)}\ \frac{1}{2}\qquad\textbf{(C)}\ \frac{2}{3}\qquad\textbf{(D)}\ \frac{5}{6}\qquad\textbf{(E)}\ 1</math>
 
<math> \textbf{(A)}\ \frac{1}{3}\qquad\textbf{(B)}\ \frac{1}{2}\qquad\textbf{(C)}\ \frac{2}{3}\qquad\textbf{(D)}\ \frac{5}{6}\qquad\textbf{(E)}\ 1</math>
Line 127: Line 138:
  
 
==Problem 13==
 
==Problem 13==
Fourteen white cubes are put together to form the fi�gure on the right. The complete surface of the �figure, including the bottom, is painted red. The �figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?
+
 
 +
Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?
  
 
<asy>
 
<asy>
Line 154: Line 166:
  
 
==Problem 14==
 
==Problem 14==
 +
 
In this addition problem, each letter stands for a different digit.  
 
In this addition problem, each letter stands for a different digit.  
  
<math> \setlength{\tabcolsep}{0.5mm}\begin{array}{cccc}&T & W & O\\ \plus{} &T & W & O\\ \hline F& O & U & R\end{array} </math>
+
<math> \setlength{\tabcolsep}{0.5mm}\begin{array}{cccc}&T & W & O\\ + &T & W & O\\ \hline F& O & U & R\end{array} </math>
  
If T = 7 and the letter O represents an even number, what is the only possible value for W?
+
If <math>T = 7</math> and the letter <math>O</math> represents an even number, what is the only possible value for <math>W</math>?
  
<math>\textbf{(A)}\ 0 \qquad
+
<math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2\qquad \textbf{(D)}\ 3\qquad \textbf{(E)}\ 4</math>
\textbf{(B)}\ 1 \qquad
 
\textbf{(C)}\ 2\qquad
 
\textbf{(D)}\ 3\qquad
 
\textbf{(E)}\ 4</math>
 
  
 
[[2003 AMC 8 Problems/Problem 14|Solution]]
 
[[2003 AMC 8 Problems/Problem 14|Solution]]
  
 
==Problem 15==
 
==Problem 15==
 +
 
A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?
 
A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?
  
Line 184: Line 194:
  
 
==Problem 16==
 
==Problem 16==
Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has <math>4</math> seats: <math>1</math> Driver seat, <math>1</math> front passenger seat, and <math>2</math> back passenger seat. Bonnie and Carlo are the only ones who know how to drive the car. How many possible seating arrangements are there?
 
  
<math>\textbf{(A)}\ 2 \qquad
+
Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has 4 seats: 1 driver's seat, 1 front passenger seat, and 2 back passenger seats. Bonnie and Carlo are the only ones who know how to drive the car. How many possible seating arrangements are there?
\textbf{(B)}\ 4 \qquad
+
 
\textbf{(C)}\ 6 \qquad
+
<math>\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 12 \qquad \textbf{(E)}\ 24</math>
\textbf{(D)}\ 12 \qquad
 
\textbf{(E)}\ 24</math>
 
  
 
[[2003 AMC 8 Problems/Problem 16|Solution]]
 
[[2003 AMC 8 Problems/Problem 16|Solution]]
  
 
==Problem 17==
 
==Problem 17==
 +
 
The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim's siblings?
 
The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim's siblings?
 +
 
<cmath> \begin{array}{c|c|c}\text{Child}&\text{Eye Color}&\text{Hair Color}\\ \hline\text{Benjamin}&\text{Blue}&\text{Black}\\ \hline\text{Jim}&\text{Brown}&\text{Blonde}\\ \hline\text{Nadeen}&\text{Brown}&\text{Black}\\ \hline\text{Austin}&\text{Blue}&\text{Blonde}\\ \hline\text{Tevyn}&\text{Blue}&\text{Black}\\ \hline\text{Sue}&\text{Blue}&\text{Blonde}\\ \hline\end{array} </cmath>
 
<cmath> \begin{array}{c|c|c}\text{Child}&\text{Eye Color}&\text{Hair Color}\\ \hline\text{Benjamin}&\text{Blue}&\text{Black}\\ \hline\text{Jim}&\text{Brown}&\text{Blonde}\\ \hline\text{Nadeen}&\text{Brown}&\text{Black}\\ \hline\text{Austin}&\text{Blue}&\text{Blonde}\\ \hline\text{Tevyn}&\text{Blue}&\text{Black}\\ \hline\text{Sue}&\text{Blue}&\text{Blonde}\\ \hline\end{array} </cmath>
<math> \textbf{(A)}\ \text{Nadeen and Austin}\qquad\textbf{(B)}\ \text{Benjamin and Sue}\qquad\textbf{(C)}\ \text{Benjamin and Austin}\qquad\textbf{(D)}\ \text{Nadeen and Tevyn}\qquad </math>
+
 
<math> \textbf{(E)}\ \text{Austin and Sue} </math>
+
<math>\textbf{(A)}\ \text{Nadeen and Austin}\qquad\textbf{(B)}\ \text{Benjamin and Sue}\qquad\textbf{(C)}\ \text{Benjamin and Austin}\qquad\textbf{(D)}\ \text{Nadeen and Tevyn}</math>
 +
 
 +
<math>\textbf{(E)}\ \text{Austin and Sue} </math>
 +
 
 +
[[2003 AMC 8 Problems/Problem 17|Solution]]
  
 
==Problem 18==
 
==Problem 18==
 +
 
Each of the twenty dots on the graph below represents one of Sarah's classmates.  Classmates who are friends are connected with a line segment.  For her birthday party, Sarah is inviting only the following:  all of her friends and all of those classmates who are friends with at least one of her friends.  How many classmates will not be invited to Sarah's party?
 
Each of the twenty dots on the graph below represents one of Sarah's classmates.  Classmates who are friends are connected with a line segment.  For her birthday party, Sarah is inviting only the following:  all of her friends and all of those classmates who are friends with at least one of her friends.  How many classmates will not be invited to Sarah's party?
 
<asy>/* AMC8 2003 #18 Problem */
 
<asy>/* AMC8 2003 #18 Problem */
Line 226: Line 240:
  
 
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7</math>
 
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7</math>
 +
 +
[[2003 AMC 8 Problems/Problem 18|Solution]]
  
 
==Problem 19==
 
==Problem 19==
How many integers between <math>1000</math> and <math>2000</math> have all three of the numbers <math>15</math>, <math>20</math>, and <math>25</math> as factors?
 
  
<math>\textbf{(A)}\ 1 \qquad
+
How many integers between 1000 and 2000 have all three of the numbers 15, 20, and 25 as factors?
\textbf{(B)}\ 2 \qquad
+
 
\textbf{(C)}\ 3 \qquad
+
<math>\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5</math>
\textbf{(D)}\ 4 \qquad
+
 
\textbf{(E)}\ 5</math>
+
[[2003 AMC 8 Problems/Problem 19|Solution]]
  
 
==Problem 20==
 
==Problem 20==
What is the measure of the acute angle formed by the hands of the clock at <math>4:20</math> PM?
 
  
<math>\textbf{(A)}\ 0 \qquad
+
What is the measure of the acute angle formed by the hands of the clock at 4:20 PM?
\textbf{(B)}\ 5 \qquad
+
 
\textbf{(C)}\ 8 \qquad
+
<math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 8 \qquad \textbf{(D)}\ 10 \qquad \textbf{(E)}\ 12</math>
\textbf{(D)}\ 10 \qquad
+
 
\textbf{(E)}\ 12</math>
+
[[2003 AMC 8 Problems/Problem 20|Solution]]
  
 
==Problem 21==
 
==Problem 21==
The area of trapezoid <math> ABCD</math> is <math> 164 \text{cm}^2</math>.  The altitude is <math> 8 \text{cm}</math>, <math> AB</math> is <math> 10 \text{cm}</math>, and <math> CD</math> is <math> 17 \text{cm}</math>.  What is <math> BC</math>, in centimeters?
+
 
 +
The area of trapezoid <math> ABCD</math> is <math>164\text{ cm}^2</math>.  The altitude is 8 cm, <math>AB</math> is 10 cm, and <math>CD</math> is 17 cm.  What is <math>BC</math>, in centimeters?
 +
 
 
<asy>/* AMC8 2003 #21 Problem */
 
<asy>/* AMC8 2003 #21 Problem */
 
size(4inch,2inch);
 
size(4inch,2inch);
Line 261: Line 277:
  
 
<math> \textbf{(A)}\ 9\qquad\textbf{(B)}\ 10\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 20</math>
 
<math> \textbf{(A)}\ 9\qquad\textbf{(B)}\ 10\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 20</math>
 +
 +
[[2003 AMC 8 Problems/Problem 21|Solution]]
  
 
==Problem 22==
 
==Problem 22==
Line 296: Line 314:
  
 
<math> \textbf{(A)}\ \text{A only}\qquad\textbf{(B)}\  \text{B only}\qquad\textbf{(C)}\  \text{C only}\qquad\textbf{(D)}\  \text{both A and B}\qquad\textbf{(E)}\  \text{all are equal}</math>
 
<math> \textbf{(A)}\ \text{A only}\qquad\textbf{(B)}\  \text{B only}\qquad\textbf{(C)}\  \text{C only}\qquad\textbf{(D)}\  \text{both A and B}\qquad\textbf{(E)}\  \text{all are equal}</math>
 +
 +
[[2003 AMC 8 Problems/Problem 22|Solution]]
  
 
==Problem 23==
 
==Problem 23==
In the pattern below, the cat (denoted as a large circle in the figures below) moves clockwise through the four squares  and the mouse (denoted as a dot in the figures below) moves counterclockwise through the eight exterior segments of the four squares.
+
In the pattern below, the cat moves clockwise through the four squares  and the mouse moves counterclockwise through the eight exterior segments of the four squares.
  
<asy>defaultpen(linewidth(0.8));
+
<center>
size(350);
+
[[Image:2003amc8prob23a.png|800px]]
path p=unitsquare;
+
</center>
int i;
 
for(i=0; i<5; i=i+1) {
 
draw(shift(3i,0)*(p^^shift(1,0)*p^^shift(0,1)*p^^shift(1,1)*p));
 
}
 
path cat=Circle((0.5,0.5), 0.3);
 
draw(shift(0,1)*cat^^shift(4,1)*cat^^shift(7,0)*cat^^shift(9,0)*cat^^shift(12,1)*cat);
 
dot((1.5,0)^^(5,0.5)^^(8,1.5)^^(10.5,2)^^(12.5,2));
 
 
 
label("1", (1,2), N);
 
label("2", (4,2), N);
 
label("3", (7,2), N);
 
label("4", (10,2), N);
 
label("5", (13,2), N);
 
</asy>
 
  
 
If the pattern is continued, where would the cat and mouse be after the 247th move?
 
If the pattern is continued, where would the cat and mouse be after the 247th move?
  
<math>\textbf{(A)}</math>
+
<center>
<asy>defaultpen(linewidth(0.8));
+
[[Image:2003amc8prob23b.png|800px]]
size(60);
+
</center>
path p=unitsquare;
 
int i=0;
 
draw(shift(3i,0)*(p^^shift(1,0)*p^^shift(0,1)*p^^shift(1,1)*p));
 
path cat=Circle((0.5,0.5), 0.3);
 
draw(shift(1,0)*cat);
 
dot((0,0.5));
 
</asy>
 
  
<math>\textbf{(B)}</math>
+
[[2003 AMC 8 Problems/Problem 23|Solution]]
<asy>defaultpen(linewidth(0.8));
 
size(60);
 
path p=unitsquare;
 
int i=0;
 
draw(shift(3i,0)*(p^^shift(1,0)*p^^shift(0,1)*p^^shift(1,1)*p));
 
path cat=Circle((0.5,0.5), 0.3);
 
draw(shift(1,1)*cat);
 
dot((0,0.5));
 
</asy>
 
 
 
<math>\textbf{(C)}</math>
 
<asy>defaultpen(linewidth(0.8));
 
size(60);
 
path p=unitsquare;
 
int i=0;
 
draw(shift(3i,0)*(p^^shift(1,0)*p^^shift(0,1)*p^^shift(1,1)*p));
 
path cat=Circle((0.5,0.5), 0.3);
 
draw(shift(1,0)*cat);
 
dot((0,1.5));
 
</asy>
 
 
 
<math>\textbf{(D)}</math>
 
<asy>defaultpen(linewidth(0.8));
 
size(60);
 
path p=unitsquare;
 
int i=0;
 
draw(shift(3i,0)*(p^^shift(1,0)*p^^shift(0,1)*p^^shift(1,1)*p));
 
path cat=Circle((0.5,0.5), 0.3);
 
draw(shift(0,0)*cat);
 
dot((0,1.5));
 
</asy>
 
 
 
<math>\textbf{(E)}</math>
 
<asy>defaultpen(linewidth(0.8));
 
size(60);
 
path p=unitsquare;
 
int i=0;
 
draw(shift(3i,0)*(p^^shift(1,0)*p^^shift(0,1)*p^^shift(1,1)*p));
 
path cat=Circle((0.5,0.5), 0.3);
 
draw(shift(0,1)*cat);
 
dot((1.5,0));
 
</asy>
 
  
 
==Problem 24==
 
==Problem 24==
A ship travels from point A to point B along a semicircular path, centered at Island X. Then it travels along a straight path from B to C. Which of these graphs best shows the ship's distance from Island X as it moves along its course?
+
A ship travels from point <math>A</math> to point <math>B</math> along a semicircular path, centered at Island <math>X</math>. Then it travels along a straight path from <math>B</math> to <math>C</math>. Which of these graphs best shows the ship's distance from Island <math>X</math> as it moves along its course?
  
 
<asy>size(150);
 
<asy>size(150);
Line 385: Line 342:
 
label("$C$", C, N);
 
label("$C$", C, N);
 
label("$B$", B, E);
 
label("$B$", B, E);
label("$A$", A, W);</asy>
+
label("$A$", A, W);
 
 
<math>\textbf{(A)}</math>
 
<asy>
 
defaultpen(fontsize(7));
 
size(80);
 
draw((0,16)--origin--(16,0), linewidth(0.9));
 
label("distance traveled", (8,0), S);
 
label(rotate(90)*"distance to X", (0,8), W);
 
draw(Arc((4,10), 4, 0, 180)^^(8,10)--(16,12));
 
</asy>
 
 
 
<math>\textbf{(B)}</math>
 
<asy>
 
defaultpen(fontsize(7));
 
size(80);
 
draw((0,16)--origin--(16,0), linewidth(0.9));
 
label("distance traveled", (8,0), S);
 
label(rotate(90)*"distance to X", (0,8), W);
 
draw(Arc((12,10), 4, 180, 360)^^(0,10)--(8,10));
 
</asy>
 
 
 
<math>\textbf{(C)}</math>
 
<asy>
 
defaultpen(fontsize(7));
 
size(80);
 
draw((0,16)--origin--(16,0), linewidth(0.9));
 
label("distance traveled", (8,0), S);
 
label(rotate(90)*"distance to X", (0,8), W);
 
draw((0,8)--(10,10)--(16,8));
 
 
</asy>
 
</asy>
  
<math>\textbf{(D)}</math>
+
<center>
<asy>
+
[[Image:2003amc8prob24ans.png|800px]]
defaultpen(fontsize(7));
+
</center>
size(80);
 
draw((0,16)--origin--(16,0), linewidth(0.9));
 
label("distance traveled", (8,0), S);
 
label(rotate(90)*"distance to X", (0,8), W);
 
draw(Arc((12,10), 4, 0, 180)^^(0,10)--(8,10));
 
</asy>
 
  
<math>\textbf{(E)}</math>
+
[[2003 AMC 8 Problems/Problem 24|Solution]]
<asy>
 
defaultpen(fontsize(7));
 
size(80);
 
draw((0,16)--origin--(16,0), linewidth(0.9));
 
label("distance traveled", (8,0), S);
 
label(rotate(90)*"distance to X", (0,8), W);
 
draw((0,6)--(6,6)--(16,10));
 
</asy>
 
  
 
==Problem 25==
 
==Problem 25==
In the figure, the area of square WXYZ is <math>25 \text{cm}^2</math>. The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In <math>\Delta ABC</math>, <math>AB = AC</math>, and when <math>\Delta ABC</math> is folded over side BC, point A coincides with O, the center of square WXYZ. What is the area of <math>\Delta ABC</math>, in square centimeters?
+
In the figure, the area of square <math>WXYZ</math> is <math>25 \text{ cm}^2</math>. The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In <math>\triangle ABC</math>, <math>AB = AC</math>, and when <math>\triangle ABC</math> is folded over side <math>\overline{BC}</math>, point <math>A</math> coincides with <math>O</math>, the center of square <math>WXYZ</math>. What is the area of <math>\triangle ABC</math>, in square centimeters?
  
 
<asy>
 
<asy>
Line 453: Line 367:
 
label("$W$",W , NE);
 
label("$W$",W , NE);
 
label("$X$", X, N);
 
label("$X$", X, N);
label("$Y$", Y, N);
+
label("$Y$", Y, S);
 
label("$Z$", Z, SE);
 
label("$Z$", Z, SE);
 
</asy>
 
</asy>
  
 
<math> \textbf{(A)}\ \frac{15}4\qquad\textbf{(B)}\ \frac{21}4\qquad\textbf{(C)}\ \frac{27}4\qquad\textbf{(D)}\ \frac{21}2\qquad\textbf{(E)}\ \frac{27}2</math>
 
<math> \textbf{(A)}\ \frac{15}4\qquad\textbf{(B)}\ \frac{21}4\qquad\textbf{(C)}\ \frac{27}4\qquad\textbf{(D)}\ \frac{21}2\qquad\textbf{(E)}\ \frac{27}2</math>
 +
 +
[[2003 AMC 8 Problems/Problem 25|Solution]]
 +
 +
==See Also==
 +
{{AMC8 box|year=2003|before=[[2002 AMC 8 Problems|2002 AMC 8]]|after=[[2004 AMC 8 Problems|2004 AMC 8]]}}
 +
* [[AMC 8]]
 +
* [[AMC 8 Problems and Solutions]]
 +
* [[Mathematics competition resources]]
 +
 +
 +
{{MAA Notice}}

Latest revision as of 18:33, 17 December 2020

Problem 1

Jamie counted the number of edges of a cube, Jimmy counted the numbers of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum?

$\mathrm{(A)}\ 12 \qquad\mathrm{(B)}\ 16 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 22 \qquad\mathrm{(E)}\ 26$

Solution

Problem 2

Which of the following numbers has the smallest prime factor?

$\mathrm{(A)}\ 55 \qquad\mathrm{(B)}\ 57 \qquad\mathrm{(C)}\ 58 \qquad\mathrm{(D)}\ 59 \qquad\mathrm{(E)}\ 61$

Solution

Problem 3

A burger at Ricky C's weighs 120 grams, of which 30 grams are filler. What percent of the burger is not filler?

$\mathrm{(A)}\ 60\% \qquad\mathrm{(B)}\ 65\% \qquad\mathrm{(C)}\ 70\% \qquad\mathrm{(D)}\ 75\% \qquad\mathrm{(E)}\ 90\%$

Solution

Problem 4

A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted 7 children and 19 wheels. How many tricycles were there?

$\mathrm{(A)}\ 2 \qquad\mathrm{(B)}\ 4 \qquad\mathrm{(C)}\ 5 \qquad\mathrm{(D)}\ 6 \qquad\mathrm{(E)}\ 7$

Solution

Problem 5

If 20% of a number is 12, what is 30% of the same number?

$\mathrm{(A)}\ 15\qquad\mathrm{(B)}\ 18 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 24 \qquad\mathrm{(E)}\ 30$

Solution

Problem 6

Given the areas of the three squares in the figure, what is the area of the interior triangle?

[asy] draw((0,0)--(-5,12)--(7,17)--(12,5)--(17,5)--(17,0)--(12,0)--(12,-12)--(0,-12)--(0,0)--(12,5)--(12,0)--cycle,linewidth(1)); label("$25$",(14.5,1),N); label("$144$",(6,-7.5),N); label("$169$",(3.5,7),N); [/asy]

$\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 30 \qquad\mathrm{(C)}\ 60 \qquad\mathrm{(D)}\ 300 \qquad\mathrm{(E)}\ 1800$

Solution

Problem 7

Blake and Jenny each took four 100-point tests. Blake averaged 78 on the four tests. Jenny scored 10 points higher than Blake on the first test, 10 points lower than him on the second test, and 20 points higher on both the third and fourth tests. What is the difference between Jenny's average and Blake's average on these four tests?

$\mathrm{(A)}\  10  \qquad\mathrm{(B)}\ 15 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 25 \qquad\mathrm{(E)}\ 40$

Solution

Problem 8

$\textbf{Bake Sale}$

(Problems 8, 9, and 10 use the data found in the accompanying paragraph and figures)

Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.

$\circ$ Art's cookies are trapezoids. [asy] size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8)); draw(origin--(5,0)--(5,3)--(2,3)--cycle); draw(rightanglemark((5,3), (5,0), origin)); label("5 in", (2.5,0), S); label("3 in", (5,1.5), E); label("3 in", (3.5,3), N); [/asy]

$\circ$ Roger's cookies are rectangles. [asy] size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8)); draw(origin--(4,0)--(4,2)--(0,2)--cycle); draw(rightanglemark((4,2), (4,0), origin)); draw(rightanglemark((0,2), origin, (4,0))); label("4 in", (2,0), S); label("2 in", (4,1), E); [/asy]

$\circ$ Paul's cookies are parallelograms. [asy] size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8)); draw(origin--(3,0)--(2.5,2)--(-0.5,2)--cycle); draw((2.5,2)--(2.5,0), dashed); draw(rightanglemark((2.5,2),(2.5,0), origin)); label("3 in", (1.5,0), S); label("2 in", (2.5,1), W); [/asy]

$\circ$ Trisha's cookies are triangles. [asy] size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8)); draw(origin--(3,0)--(3,4)--cycle); draw(rightanglemark((3,4),(3,0), origin)); label("3 in", (1.5,0), S); label("4 in", (3,2), E); [/asy]

Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Who gets the fewest cookies from one batch of cookie dough?

$\textbf{(A)}\ \text{Art}\qquad\textbf{(B)}\ \text{Roger}\qquad\textbf{(C)}\ \text{Paul}\qquad\textbf{(D)}\ \text{Trisha}\qquad\textbf{(E)}\ \text{There is a tie for fewest.}$

Solution

Problem 9

Each friend uses the same amount of dough, and Art makes exactly $12$ cookies. Art's cookies sell for $60$ cents each. To earn the same amount from a single batch, how much should one of Roger's cookies cost in cents?

$\textbf{(A)}\ 18\qquad\textbf{(B)}\ 25\qquad\textbf{(C)}\ 40\qquad\textbf{(D)}\ 75\qquad\textbf{(E)}\ 90$

Solution

Problem 10

How many cookies will be in one batch of Trisha's cookies?

$\textbf{(A)}\ 10\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 16\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 24$

Solution

Problem 11

Business is a little slow at Lou's Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday's prices by 10%. Over the weekend, Lou advertises the sale: "Ten percent off the listed price. Sale starts Monday." How much does a pair of shoes cost on Monday that cost 40 dollars on Thursday?

$\textbf{(A)}\ 36\qquad\textbf{(B)}\ 39.60\qquad\textbf{(C)}\ 40\qquad\textbf{(D)}\ 40.40\qquad\textbf{(E)}\ 44$

Solution

Problem 12

When a fair six-sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the numbers on the five faces that can be seen is divisible by 6?

$\textbf{(A)}\ \frac{1}{3}\qquad\textbf{(B)}\ \frac{1}{2}\qquad\textbf{(C)}\ \frac{2}{3}\qquad\textbf{(D)}\ \frac{5}{6}\qquad\textbf{(E)}\ 1$

Solution

Problem 13

Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?

[asy] import three; defaultpen(linewidth(0.8)); real r=0.5; currentprojection=orthographic(3/4,8/15,7/15); draw(unitcube, white, thick(), nolight); draw(shift(1,0,0)*unitcube, white, thick(), nolight); draw(shift(2,0,0)*unitcube, white, thick(), nolight); draw(shift(0,0,1)*unitcube, white, thick(), nolight); draw(shift(2,0,1)*unitcube, white, thick(), nolight); draw(shift(0,1,0)*unitcube, white, thick(), nolight); draw(shift(2,1,0)*unitcube, white, thick(), nolight); draw(shift(0,2,0)*unitcube, white, thick(), nolight); draw(shift(2,2,0)*unitcube, white, thick(), nolight); draw(shift(0,3,0)*unitcube, white, thick(), nolight); draw(shift(0,3,1)*unitcube, white, thick(), nolight); draw(shift(1,3,0)*unitcube, white, thick(), nolight); draw(shift(2,3,0)*unitcube, white, thick(), nolight); draw(shift(2,3,1)*unitcube, white, thick(), nolight);[/asy]

$\textbf{(A)}\ 4\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 12$

Solution

Problem 14

In this addition problem, each letter stands for a different digit.

$\setlength{\tabcolsep}{0.5mm}\begin{array}{cccc}&T & W & O\\ + &T & W & O\\ \hline F& O & U & R\end{array}$

If $T = 7$ and the letter $O$ represents an even number, what is the only possible value for $W$?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2\qquad \textbf{(D)}\ 3\qquad \textbf{(E)}\ 4$

Solution

Problem 15

A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?

[asy] defaultpen(linewidth(0.8)); path p=unitsquare; draw(p^^shift(0,1)*p^^shift(1,0)*p); draw(shift(4,0)*p^^shift(5,0)*p^^shift(5,1)*p); label("FRONT", (1,0), S); label("SIDE", (5,0), S);[/asy]

$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7$

Solution

Problem 16

Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has 4 seats: 1 driver's seat, 1 front passenger seat, and 2 back passenger seats. Bonnie and Carlo are the only ones who know how to drive the car. How many possible seating arrangements are there?

$\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 12 \qquad \textbf{(E)}\ 24$

Solution

Problem 17

The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim's siblings?

\[\begin{array}{c|c|c}\text{Child}&\text{Eye Color}&\text{Hair Color}\\ \hline\text{Benjamin}&\text{Blue}&\text{Black}\\ \hline\text{Jim}&\text{Brown}&\text{Blonde}\\ \hline\text{Nadeen}&\text{Brown}&\text{Black}\\ \hline\text{Austin}&\text{Blue}&\text{Blonde}\\ \hline\text{Tevyn}&\text{Blue}&\text{Black}\\ \hline\text{Sue}&\text{Blue}&\text{Blonde}\\ \hline\end{array}\]

$\textbf{(A)}\ \text{Nadeen and Austin}\qquad\textbf{(B)}\ \text{Benjamin and Sue}\qquad\textbf{(C)}\ \text{Benjamin and Austin}\qquad\textbf{(D)}\ \text{Nadeen and Tevyn}$

$\textbf{(E)}\ \text{Austin and Sue}$

Solution

Problem 18

Each of the twenty dots on the graph below represents one of Sarah's classmates. Classmates who are friends are connected with a line segment. For her birthday party, Sarah is inviting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not be invited to Sarah's party? [asy]/* AMC8 2003 #18 Problem */ pair a=(102,256), b=(68,131), c=(162,101), d=(134,150); pair e=(269,105), f=(359,104), g=(303,12), h=(579,211); pair i=(534, 342), j=(442,432), k=(374,484), l=(278,501); pair m=(282,411), n=(147,451), o=(103,437), p=(31,373); pair q=(419,175), r=(462,209), s=(477,288), t=(443,358); pair oval=(282,303); draw(l--m--n--cycle); draw(p--oval); draw(o--oval); draw(b--d--oval); draw(c--d--e--oval); draw(e--f--g--h--i--j--oval); draw(k--oval); draw(q--oval); draw(s--oval); draw(r--s--t--oval); dot(a); dot(b); dot(c); dot(d); dot(e); dot(f); dot(g); dot(h); dot(i); dot(j); dot(k); dot(l); dot(m); dot(n); dot(o); dot(p); dot(q); dot(r); dot(s); dot(t); filldraw(yscale(.5)*Circle((282,606),80),white,black); label(scale(0.75)*"Sarah", oval);[/asy]

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7$

Solution

Problem 19

How many integers between 1000 and 2000 have all three of the numbers 15, 20, and 25 as factors?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5$

Solution

Problem 20

What is the measure of the acute angle formed by the hands of the clock at 4:20 PM?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 8 \qquad \textbf{(D)}\ 10 \qquad \textbf{(E)}\ 12$

Solution

Problem 21

The area of trapezoid $ABCD$ is $164\text{ cm}^2$. The altitude is 8 cm, $AB$ is 10 cm, and $CD$ is 17 cm. What is $BC$, in centimeters?

[asy]/* AMC8 2003 #21 Problem */ size(4inch,2inch); draw((0,0)--(31,0)--(16,8)--(6,8)--cycle); draw((11,8)--(11,0), linetype("8 4")); draw((11,1)--(12,1)--(12,0)); label("$A$", (0,0), SW); label("$D$", (31,0), SE); label("$B$", (6,8), NW); label("$C$", (16,8), NE); label("10", (3,5), W); label("8", (11,4), E); label("17", (22.5,5), E);[/asy]

$\textbf{(A)}\ 9\qquad\textbf{(B)}\ 10\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 20$

Solution

Problem 22

The following figures are composed of squares and circles. Which figure has a shaded region with largest area? [asy]/* AMC8 2003 #22 Problem */ size(3inch, 2inch); unitsize(1cm); pen outline = black+linewidth(1); filldraw((0,0)--(2,0)--(2,2)--(0,2)--cycle, mediumgrey, outline); filldraw(shift(3,0)*((0,0)--(2,0)--(2,2)--(0,2)--cycle), mediumgrey, outline); filldraw(Circle((7,1), 1), mediumgrey, black+linewidth(1)); filldraw(Circle((1,1), 1), white, outline); filldraw(Circle((3.5,.5), .5), white, outline); filldraw(Circle((4.5,.5), .5), white, outline); filldraw(Circle((3.5,1.5), .5), white, outline); filldraw(Circle((4.5,1.5), .5), white, outline); filldraw((6.3,.3)--(7.7,.3)--(7.7,1.7)--(6.3,1.7)--cycle, white, outline); label("A", (1, 2), N); label("B", (4, 2), N); label("C", (7, 2), N); draw((0,-.5)--(.5,-.5), BeginArrow); draw((1.5, -.5)--(2, -.5), EndArrow); label("2 cm", (1, -.5));  draw((3,-.5)--(3.5,-.5), BeginArrow); draw((4.5, -.5)--(5, -.5), EndArrow); label("2 cm", (4, -.5));  draw((6,-.5)--(6.5,-.5), BeginArrow); draw((7.5, -.5)--(8, -.5), EndArrow); label("2 cm", (7, -.5));  draw((6,1)--(6,-.5), linetype("4 4")); draw((8,1)--(8,-.5), linetype("4 4"));[/asy]

$\textbf{(A)}\ \text{A only}\qquad\textbf{(B)}\  \text{B only}\qquad\textbf{(C)}\  \text{C only}\qquad\textbf{(D)}\  \text{both A and B}\qquad\textbf{(E)}\  \text{all are equal}$

Solution

Problem 23

In the pattern below, the cat moves clockwise through the four squares and the mouse moves counterclockwise through the eight exterior segments of the four squares.

2003amc8prob23a.png

If the pattern is continued, where would the cat and mouse be after the 247th move?

2003amc8prob23b.png

Solution

Problem 24

A ship travels from point $A$ to point $B$ along a semicircular path, centered at Island $X$. Then it travels along a straight path from $B$ to $C$. Which of these graphs best shows the ship's distance from Island $X$ as it moves along its course?

[asy]size(150); pair X=origin, A=(-5,0), B=(5,0), C=(0,5); draw(Arc(X, 5, 180, 360)^^B--C); dot(X); label("$X$", X, NE); label("$C$", C, N); label("$B$", B, E); label("$A$", A, W); [/asy]

2003amc8prob24ans.png

Solution

Problem 25

In the figure, the area of square $WXYZ$ is $25 \text{ cm}^2$. The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In $\triangle ABC$, $AB = AC$, and when $\triangle ABC$ is folded over side $\overline{BC}$, point $A$ coincides with $O$, the center of square $WXYZ$. What is the area of $\triangle ABC$, in square centimeters?

[asy] defaultpen(fontsize(8)); size(225); pair Z=origin, W=(0,10), X=(10,10), Y=(10,0), O=(5,5), B=(-4,8), C=(-4,2), A=(-13,5); draw((-4,0)--Y--X--(-4,10)--cycle); draw((0,-2)--(0,12)--(-2,12)--(-2,8)--B--A--C--(-2,2)--(-2,-2)--cycle); dot(O); label("$A$", A, NW); label("$O$", O, NE); label("$B$", B, SW); label("$C$", C, NW); label("$W$",W , NE); label("$X$", X, N); label("$Y$", Y, S); label("$Z$", Z, SE); [/asy]

$\textbf{(A)}\ \frac{15}4\qquad\textbf{(B)}\ \frac{21}4\qquad\textbf{(C)}\ \frac{27}4\qquad\textbf{(D)}\ \frac{21}2\qquad\textbf{(E)}\ \frac{27}2$

Solution

See Also

2003 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
2002 AMC 8
Followed by
2004 AMC 8
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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