Difference between revisions of "2003 AMC 8 Problems"

Latest revision as of 11:02, 19 February 2024

2003 AMC 8 (Answer Key) Printable versions: Wiki • AoPS Resources • PDF
Instructions This is a 25-question, multiple choice test. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct. You will receive 1 point for each correct answer. There is no penalty for wrong answers. No aids are permitted other than plain scratch paper, writing utensils, ruler, and erasers. In particular, graph paper, compass, protractor, calculators, computers, smartwatches, and smartphones are not permitted. Rules Figures are not necessarily drawn to scale. You will have 40 minutes working time to complete the test.
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

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.

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

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$", A, W); [/asy]$

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

2003 AMC 8 (Problems • Answer Key • Resources)
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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Difference between revisions of "2003 AMC 8 Problems"

Latest revision as of 11:02, 19 February 2024

Contents

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

See Also

@@ Line 1: / Line 1: @@
+{{AMC8 Problems|year=2003|}}
 ==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?
 <math>\mathrm{(A)}\ 12 \qquad\mathrm{(B)}\ 16 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 22 \qquad\mathrm{(E)}\ 26</math>
@@ Line 14: / Line 15: @@
 ==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>
@@ Line 22: / Line 22: @@
 ==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>
@@ Line 29: / Line 29: @@
 ==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>
@@ Line 36: / Line 36: @@
 ==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>
@@ Line 43: / Line 50: @@
 ==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>
@@ Line 50: / Line 57: @@
 ==Problem 8==
-'''Bake Sale''' 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>\textbf{Bake Sale}</math>
-<math>\circ</math> Art's cookies are trapezoids:
+(Problems 8, 9, and 10 use the data found in the accompanying paragraph and figures)
-<asy>size(80);defaultpen(linewidth(0.8));defaultpen(fontsize(8));
+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.
+<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>
+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(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>
+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((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>
+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(rightanglemark((3,4),(3,0), origin));
 label("3 in", (1.5,0), S);
-label("4 in", (3,2), E);</asy>
+label("4 in", (3,2), E);
+</asy>
-Who gets the fewest cookies from one batch of cookie dough?
+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?
-<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]]
 ==Problem 9==
-'''Bake Sale''' 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:
-<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>
-<math>\circ</math> 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>
-<math>\circ</math> 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>
-<math>\circ</math> 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 <math>12</math> cookies. Art's cookies sell for <math>60</math> cents each. To earn the same amount from a single batch, how much should one of Roger's cookies cost in cents?
@@ Line 131: / Line 116: @@
 ==Problem 10==
-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.
-<math>\circ</math> 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>
-<math>\circ</math> 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>
-<math>\circ</math> 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>
-<math>\circ</math> 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>
 How many cookies will be in one batch of Trisha's cookies?
@@ Line 173: / Line 123: @@
 ==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>
@@ Line 184: / Line 131: @@
 ==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>
@@ Line 193: / Line 139: @@
 ==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?
@@ Line 220: / Line 167: @@
 ==Problem 14==
 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]]
 ==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?
@@ Line 250: / Line 195: @@
 ==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]]
 ==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?
 <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==
 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 */
@@ Line 298: / Line 245: @@
 ==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==
-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==
-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 */
 size(4inch,2inch);
@@ Line 376: / Line 319: @@
 ==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?
-<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>
-<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>
 [[2003 AMC 8 Problems/Problem 23|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?
+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);
@@ Line 465: / Line 343: @@
 label("$C$", C, N);
 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>
+<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((0,8)--(10,10)--(16,8));
-</asy>
-<math>\textbf{(D)}</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, 0, 180)^^(0,10)--(8,10));
-</asy>
-<math>\textbf{(E)}</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((0,6)--(6,6)--(16,10));
-</asy>
 [[2003 AMC 8 Problems/Problem 24|Solution]]
 ==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>
@@ Line 535: / Line 368: @@
 label("$W$",W , NE);
 label("$X$", X, N);
-label("$Y$", Y, N);
+label("$Y$", Y, S);
 label("$Z$", Z, SE);
 </asy>
@@ Line 542: / Line 375: @@
 [[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}}