Difference between revisions of "2001 AMC 8 Problems"

Latest revision as of 08:51, 19 June 2024

2001 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

John's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he need to do his job?

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

Solution

Problem 2

I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?

$\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 12$

Solution

Problem 3

Granny Smith has $63. Elberta has $2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars does Elberta have?

$\text{(A)}\ 17 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 19 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 23$

Solution

Problem 4

The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 9$

Solution

Problem 5

On a dark and stormy night Snoopy suddenly saw a flash of lightning. Ten seconds later he heard the sound of thunder. The speed of sound is 1088 feet per second and one mile is 5280 feet. Estimate, to the nearest half-mile, how far Snoopy was from the flash of lightning.

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

Solution

Problem 6

Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees?

$\text{(A)}\ 90 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 105 \qquad \text{(D)}\ 120 \qquad \text{(E)}\ 140$

Solution

Problems 7, 8 and 9 are about these kites.

To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram below. For her small kite Genevieve draws the kite on a one-inch grid. For the large kite she triples both the height and width of the entire grid. $[asy] for (int a = 0; a < 7; ++a) { for (int b = 0; b < 8; ++b) { dot((a,b)); } } draw((3,0)--(0,5)--(3,7)--(6,5)--cycle); [/asy]$

Problem 7

What is the number of square inches in the area of the small kite?

$\text{(A)}\ 21 \qquad \text{(B)}\ 22 \qquad \text{(C)}\ 23 \qquad \text{(D)}\ 24 \qquad \text{(E)}\ 25$

Solution

Problem 8

Genevieve puts bracing on her large kite in the form of cross-connecting opposite corners of the kite. How many inches of bracing material does she need?

$\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 35 \qquad \text{(D)}\ 38 \qquad \text{(E)}\ 39$

Solution

Problem 9

The large kite is covered with gold foil. The foil is cut from a rectangular piece that just covers the entire grid. How many square inches of waste material are cut off from the four corners?

$\text{(A)}\ 63 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 180 \qquad \text{(D)}\ 189 \qquad \text{(E)}\ 264$

Solution

Problem 10

A collector offers to buy state quarters for 2000% of their face value. At that rate how much will Bryden get for his four state quarters?

$\text{(A)}\ 20\text{ dollars} \qquad \text{(B)}\ 50\text{ dollars} \qquad \text{(C)}\ 200\text{ dollars} \qquad \text{(D)}\ 500\text{ dollars} \qquad \text{(E)}\ 2000\text{ dollars}$

Solution

Problem 11

Points $A$ , $B$ , $C$ and $D$ have these coordinates: $A(3,2)$ , $B(3,-2)$ , $C(-3,-2)$ and $D(-3, 0)$ . The area of quadrilateral $ABCD$ is

$[asy] for (int i = -4; i <= 4; ++i) { for (int j = -4; j <= 4; ++j) { dot((i,j)); } } draw((0,-4)--(0,4),linewidth(1)); draw((-4,0)--(4,0),linewidth(1)); for (int i = -4; i <= 4; ++i) { draw((i,-1/3)--(i,1/3),linewidth(0.5)); draw((-1/3,i)--(1/3,i),linewidth(0.5)); } [/asy]$

$\text{(A)}\ 12 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 24$

Solution

Problem 12

If $a\otimes b = \dfrac{a + b}{a - b}$ , then $(6\otimes 4)\otimes 3 =$

$\text{(A)}\ 4 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 15 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 72$

Solution

Problem 13

Of the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer blueberry. Half of the remaining students prefer cherry pie and half prefer lemon. For Richelle's pie graph showing this data, how many degrees should she use for cherry pie?

$\text{(A)}\ 10 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 50 \qquad \text{(E)}\ 72$

Solution

Problem 14

Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose?

Meat: beef, chicken, pork
Vegetables: baked beans, corn, potatoes, tomatoes
Dessert: brownies, chocolate cake, chocolate pudding, ice cream

$\text{(A)}\ 4 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 72 \qquad \text{(D)}\ 80 \qquad \text{(E)}\ 144$

Solution

Problem 15

Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later Christen joined him and peeled at the rate of 5 potatoes per minute. When they finished, how many potatoes had Christen peeled?

$\text{(A)}\ 20 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 33 \qquad \text{(E)}\ 40$

Solution

Problem 16

A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new rectangles are formed, a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?

$[asy] draw((0,8)--(0,0)--(4,0)--(4,8)--(0,8)--(3.5,8.5)--(3.5,8)); draw((2,-1)--(2,9),dashed); [/asy]$

$\text{(A)}\ \dfrac{1}{3} \qquad \text{(B)}\ \dfrac{1}{2} \qquad \text{(C)}\ \dfrac{3}{4} \qquad \text{(D)}\ \dfrac{4}{5} \qquad \text{(E)}\ \dfrac{5}{6}$

Solution

Problem 17

For the game show Who Wants To Be A Millionaire?, the dollar values of each question are shown in the following table (where K = 1000).

$\begin{tabular}{rccccccccccccccc} \text{Question} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\ \text{Value} & 100 & 200 & 300 & 500 & 1\text{K} & 2\text{K} & 4\text{K} & 8\text{K} & 16\text{K} & 32\text{K} & 64\text{K} & 125\text{K} & 250\text{K} & 500\text{K} & 1000\text{K} \end{tabular}$

Between which two questions is the percent increase of the value the smallest?

$\text{(A)}\ \text{From 1 to 2} \qquad \text{(B)}\ \text{From 2 to 3} \qquad \text{(C)}\ \text{From 3 to 4} \qquad \text{(D)}\ \text{From 11 to 12} \qquad \text{(E)}\ \text{From 14 to 15}$

Solution

Problem 18

Two dice are thrown. What is the probability that the product of the two numbers is a multiple of 5?

$\text{(A)}\ \dfrac{1}{36} \qquad \text{(B)}\ \dfrac{1}{18} \qquad \text{(C)}\ \dfrac{1}{6} \qquad \text{(D)}\ \dfrac{11}{36} \qquad \text{(E)}\ \dfrac{1}{3}$

Solution

Problem 19

Car M traveled at a constant speed for a given time. This is shown by the dashed line. Car N traveled at twice the speed for the same distance. If Car N's speed and time are shown as solid line, which graph illustrates this?

$[asy] unitsize(12); draw((0,9)--(0,0)--(9,0)); label("time",(4.5,0),S); label("s",(0,7),W); label("p",(0,6),W); label("e",(0,5),W); label("e",(0,4),W); label("d",(0,3),W); label("(A)",(-1,9),NW); draw((0,4)--(4,4),dashed); label("M",(4,4),E); draw((0,8)--(4,8),linewidth(1)); label("N",(4,8),E); draw((15,9)--(15,0)--(24,0)); label("time",(19.5,0),S); label("s",(15,7),W); label("p",(15,6),W); label("e",(15,5),W); label("e",(15,4),W); label("d",(15,3),W); label("(B)",(14,9),NW); draw((15,4)--(19,4),dashed); label("M",(19,4),E); draw((15,8)--(23,8),linewidth(1)); label("N",(23,8),E); draw((30,9)--(30,0)--(39,0)); label("time",(34.5,0),S); label("s",(30,7),W); label("p",(30,6),W); label("e",(30,5),W); label("e",(30,4),W); label("d",(30,3),W); label("(C)",(29,9),NW); draw((30,4)--(34,4),dashed); label("M",(34,4),E); draw((30,2)--(34,2),linewidth(1)); label("N",(34,2),E); draw((0,-6)--(0,-15)--(9,-15)); label("time",(4.5,-15),S); label("s",(0,-8),W); label("p",(0,-9),W); label("e",(0,-10),W); label("e",(0,-11),W); label("d",(0,-12),W); label("(D)",(-1,-6),NW); draw((0,-11)--(4,-11),dashed); label("M",(4,-11),E); draw((0,-7)--(2,-7),linewidth(1)); label("N",(2,-7),E); draw((15,-6)--(15,-15)--(24,-15)); label("time",(19.5,-15),S); label("s",(15,-8),W); label("p",(15,-9),W); label("e",(15,-10),W); label("e",(15,-11),W); label("d",(15,-12),W); label("(E)",(14,-6),NW); draw((15,-11)--(19,-11),dashed); label("M",(19,-11),E); draw((15,-13)--(23,-13),linewidth(1)); label("N",(23,-13),E); [/asy]$

Solution

Problem 20

Kaleana shows her test score to Quay, Marty and Shana, but the others keep theirs hidden. Quay thinks, "At least two of us have the same score." Marty thinks, "I didn't get the lowest score." Shana thinks, "I didn't get the highest score." List the scores from lowest to highest for Marty (M), Quay (Q) and Shana (S).

$\text{(A)}\ \text{S,Q,M} \qquad \text{(B)}\ \text{Q,M,S} \qquad \text{(C)}\ \text{Q,S,M} \qquad \text{(D)}\ \text{M,S,Q} \qquad \text{(E)}\ \text{S,M,Q}$

Solution

Problem 21

The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest of these five integers is

$\text{(A)}\ 19 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 35 \qquad \text{(E)}\ 40$

Solution

Problem 22

On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and each incorrect answer is worth 0 points. Which of the following scores is NOT possible?

$\text{(A)}\ 90 \qquad \text{(B)}\ 91 \qquad \text{(C)}\ 92 \qquad \text{(D)}\ 95 \qquad \text{(E)}\ 97$

Solution

Problem 23

Points $R$ , $S$ and $T$ are vertices of an equilateral triangle, and points $X$ , $Y$ and $Z$ are midpoints of its sides. How many noncongruent triangles can be drawn using any three of these six points as vertices?

$[asy] pair SS,R,T,X,Y,Z; SS = (2,2*sqrt(3)); R = (0,0); T = (4,0); X = (2,0); Y = (1,sqrt(3)); Z = (3,sqrt(3)); dot(SS); dot(R); dot(T); dot(X); dot(Y); dot(Z); label("$S$",SS,N); label("$R$",R,SW); label("$T$",T,SE); label("$X$",X,S); label("$Y$",Y,NW); label("$Z$",Z,NE); [/asy]$

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 20$

Solution

Problem 24

Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. There are 2 red-white pairs. How many white pairs coincide?

$[asy] draw((0,0)--(4,4*sqrt(3))); draw((1,-sqrt(3))--(5,3*sqrt(3))); draw((2,-2*sqrt(3))--(6,2*sqrt(3))); draw((3,-3*sqrt(3))--(7,sqrt(3))); draw((4,-4*sqrt(3))--(8,0)); draw((8,0)--(4,4*sqrt(3))); draw((7,-sqrt(3))--(3,3*sqrt(3))); draw((6,-2*sqrt(3))--(2,2*sqrt(3))); draw((5,-3*sqrt(3))--(1,sqrt(3))); draw((4,-4*sqrt(3))--(0,0)); draw((3,3*sqrt(3))--(5,3*sqrt(3))); draw((2,2*sqrt(3))--(6,2*sqrt(3))); draw((1,sqrt(3))--(7,sqrt(3))); draw((-1,0)--(9,0)); draw((1,-sqrt(3))--(7,-sqrt(3))); draw((2,-2*sqrt(3))--(6,-2*sqrt(3))); draw((3,-3*sqrt(3))--(5,-3*sqrt(3))); [/asy]$

$\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 9$

Solution

Problem 25

There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly once. Only one of these four-digit numbers is a multiple of another one. Which of the following is it?

$\text{(A)}\ 5724 \qquad \text{(B)}\ 7245 \qquad \text{(C)}\ 7254 \qquad \text{(D)}\ 7425 \qquad \text{(E)}\ 7542$

Solution

2001 AMC 8 (Problems • Answer Key • Resources)
Preceded by 2000 AMC 8	Followed by 2002 AMC 8
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All AJHSME/AMC 8 Problems and Solutions

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Difference between revisions of "2001 AMC 8 Problems"

Latest revision as of 08:51, 19 June 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=2001|}}
 ==Problem 1==
-Casey's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he need to do his job?
-A) 4
+John's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he need to do his job?
-B) 6
-C) 8
+<math> \mathrm{(A) \ 4 } \qquad \mathrm{(B) \ 6 } \qquad \mathrm{(C) \ 8 } \qquad \mathrm{(D) \ 10 } \qquad \mathrm{(E) \ 12 }  </math>
-D) 10
-E) 12
+[[2001 AMC 8 Problems/Problem 1 | Solution]]
-[[AMC-8 2001 Problems/Problem 1 | Solution]]
 ==Problem 2==
+I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?
-[[AMC-8 2001 Problems/Problem 2 | Solution]]
+<math>\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 12</math>
+[[2001 AMC 8 Problems/Problem 2 | Solution]]
 ==Problem 3==
+Granny Smith has \$63. Elberta has \$2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars does Elberta have?
+<math>\text{(A)}\ 17 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 19 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 23</math>
+[[2001 AMC 8 Problems/Problem 3 | Solution]]
-[[AMC-8 2001 Problems/Problem 3 | Solution]]
 ==Problem 4==
+The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible '''even''' five-digit number. The digit in the tens place is
+<math>\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 9</math>
+[[2001 AMC 8 Problems/Problem 4 | Solution]]
-[[AMC-8 2001 Problems/Problem 4 | Solution]]
 ==Problem 5==
+On a dark and stormy night Snoopy suddenly saw a flash of lightning. Ten seconds later he heard the sound of thunder. The speed of sound is 1088 feet per second and one mile is 5280 feet. Estimate, to the nearest half-mile, how far Snoopy was from the flash of lightning.
+<math>\text{(A)}\ 1 \qquad \text{(B)}\ 1\frac{1}{2} \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 2\frac{1}{2} \qquad \text{(E)}\ 3</math>
+[[2001 AMC 8 Problems/Problem 5 | Solution]]
-[[AMC-8 2001 Problems/Problem 5 | Solution]]
 ==Problem 6==
+Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees?
-[[AMC-8 2001 Problems/Problem 6 | Solution]]
+<math>\text{(A)}\ 90 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 105 \qquad \text{(D)}\ 120 \qquad \text{(E)}\ 140</math>
-==Problem 7==
+[[2001 AMC 8 Problems/Problem 6 | Solution]]
-[[AMC-8 2001 Problems/Problem 7 | Solution]]
-==Problem 8==
+''Problems 7, 8 and 9 are about these kites.''
-[[AMC-8 2001 Problems/Problem 8 | Solution]]
+To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram below. For her small kite Genevieve draws the kite on a one-inch grid. For the large kite she triples both the height and width of the entire grid.
-==Problem 9==
+<asy>
+for (int a = 0; a < 7; ++a) { for (int b = 0; b < 8; ++b) { dot((a,b)); } }
+draw((3,0)--(0,5)--(3,7)--(6,5)--cycle);
+</asy>
+===Problem 7===
+What is the number of square inches in the area of the small kite?
+<math>\text{(A)}\ 21 \qquad \text{(B)}\ 22 \qquad \text{(C)}\ 23 \qquad \text{(D)}\ 24 \qquad \text{(E)}\ 25</math>
+[[2001 AMC 8 Problems/Problem 7 | Solution]]
+===Problem 8===
+Genevieve puts bracing on her large kite in the form of cross-connecting opposite corners of the kite. How many inches of bracing material does she need?
+<math>\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 35 \qquad \text{(D)}\ 38 \qquad \text{(E)}\ 39</math>
+[[2001 AMC 8 Problems/Problem 8 | Solution]]
+===Problem 9===
+The large kite is covered with gold foil. The foil is cut from a rectangular piece that just covers the entire grid. How many square inches of waste material are cut off from the four corners?
+<math>\text{(A)}\ 63 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 180 \qquad \text{(D)}\ 189 \qquad \text{(E)}\ 264</math>
+[[2001 AMC 8 Problems/Problem 9 | Solution]]
-[[AMC-8 2001 Problems/Problem 9 | Solution]]
 ==Problem 10==
+A collector offers to buy state quarters for 2000% of their face value. At that rate how much will Bryden get for his four state quarters?
+<math>\text{(A)}\ 20\text{ dollars} \qquad \text{(B)}\ 50\text{ dollars} \qquad \text{(C)}\ 200\text{ dollars} \qquad \text{(D)}\ 500\text{ dollars} \qquad \text{(E)}\ 2000\text{ dollars}</math>
+[[2001 AMC 8 Problems/Problem 10 | Solution]]
-[[AMC-8 2001 Problems/Problem 10 | Solution]]
 ==Problem 11==
+Points <math>A</math>, <math>B</math>, <math>C</math> and <math>D</math> have these coordinates: <math>A(3,2)</math>, <math>B(3,-2)</math>, <math>C(-3,-2)</math> and <math>D(-3, 0)</math>. The area of quadrilateral <math>ABCD</math> is
+<asy>
+for (int i = -4; i <= 4; ++i)
+{
+for (int j = -4; j <= 4; ++j)
+{
+dot((i,j));
+}
+}
+draw((0,-4)--(0,4),linewidth(1));
+draw((-4,0)--(4,0),linewidth(1));
+for (int i = -4; i <= 4; ++i)
+{
+draw((i,-1/3)--(i,1/3),linewidth(0.5));
+draw((-1/3,i)--(1/3,i),linewidth(0.5));
+}
+</asy>
+<math>\text{(A)}\ 12 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 24</math>
+[[2001 AMC 8 Problems/Problem 11 | Solution]]
-[[AMC-8 2001 Problems/Problem 11 | Solution]]
 ==Problem 12==
+If <math>a\otimes b = \dfrac{a + b}{a - b}</math>, then <math>(6\otimes 4)\otimes 3 = </math>
+<math>\text{(A)}\ 4 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 15 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 72</math>
+[[2001 AMC 8 Problems/Problem 12 | Solution]]
-[[AMC-8 2001 Problems/Problem 12 | Solution]]
 ==Problem 13==
+Of the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer blueberry. Half of the remaining students prefer cherry pie and half prefer lemon. For Richelle's pie graph showing this data, how many degrees should she use for cherry pie?
+<math>\text{(A)}\ 10 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 50 \qquad \text{(E)}\ 72</math>
+[[2001 AMC 8 Problems/Problem 13 | Solution]]
-[[AMC-8 2001 Problems/Problem 13 | Solution]]
 ==Problem 14==
+Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose?
+*Meat: beef, chicken, pork
+*Vegetables: baked beans, corn, potatoes, tomatoes
+*Dessert: brownies, chocolate cake, chocolate pudding, ice cream
+<math>\text{(A)}\ 4 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 72 \qquad \text{(D)}\ 80 \qquad \text{(E)}\ 144</math>
+[[2001 AMC 8 Problems/Problem 14 | Solution]]
-[[AMC-8 2001 Problems/Problem 14 | Solution]]
 ==Problem 15==
+Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later Christen joined him and peeled at the rate of 5 potatoes per minute. When they finished, how many potatoes had Christen peeled?
+<math>\text{(A)}\ 20 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 33 \qquad \text{(E)}\ 40</math>
+[[2001 AMC 8 Problems/Problem 15 | Solution]]
-[[AMC-8 2001 Problems/Problem 15 | Solution]]
 ==Problem 16==
+A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new rectangles are formed, a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?
+<asy>
+draw((0,8)--(0,0)--(4,0)--(4,8)--(0,8)--(3.5,8.5)--(3.5,8));
+draw((2,-1)--(2,9),dashed);
+</asy>
+<math>\text{(A)}\ \dfrac{1}{3} \qquad \text{(B)}\ \dfrac{1}{2} \qquad \text{(C)}\ \dfrac{3}{4} \qquad \text{(D)}\ \dfrac{4}{5} \qquad \text{(E)}\ \dfrac{5}{6}</math>
+[[2001 AMC 8 Problems/Problem 16 | Solution]]
-[[AMC-8 2001 Problems/Problem 16 | Solution]]
 ==Problem 17==
+For the game show ''Who Wants To Be A Millionaire?'', the dollar values of each question are shown in the following table (where K = 1000).
+<cmath>\begin{tabular}{rccccccccccccccc}
+\text{Question} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
+\text{Value} & 100 & 200 & 300 & 500 & 1\text{K} & 2\text{K} & 4\text{K} & 8\text{K} & 16\text{K} & 32\text{K} & 64\text{K} & 125\text{K} & 250\text{K} & 500\text{K} & 1000\text{K}
+\end{tabular}</cmath>
+Between which two questions is the percent increase of the value the smallest?
+<math>\text{(A)}\ \text{From 1 to 2} \qquad \text{(B)}\ \text{From 2 to 3} \qquad \text{(C)}\ \text{From 3 to 4} \qquad \text{(D)}\ \text{From 11 to 12} \qquad \text{(E)}\ \text{From 14 to 15}</math>
+[[2001 AMC 8 Problems/Problem 17 | Solution]]
-[[AMC-8 2001 Problems/Problem 17 | Solution]]
 ==Problem 18==
+Two dice are thrown. What is the probability that the product of the two numbers is a multiple of 5?
+<math>\text{(A)}\ \dfrac{1}{36} \qquad \text{(B)}\ \dfrac{1}{18} \qquad \text{(C)}\ \dfrac{1}{6} \qquad \text{(D)}\ \dfrac{11}{36} \qquad \text{(E)}\ \dfrac{1}{3}</math>
+[[2001 AMC 8 Problems/Problem 18 | Solution]]
-[[AMC-8 2001 Problems/Problem 18 | Solution]]
 ==Problem 19==
+Car M traveled at a constant speed for a given time. This is shown by the dashed line. Car N traveled at twice the speed for the same distance. If Car N's speed and time are shown as solid line, which graph illustrates this?
+<asy>
+unitsize(12);
+draw((0,9)--(0,0)--(9,0));
+label("time",(4.5,0),S);
+label("s",(0,7),W); label("p",(0,6),W); label("e",(0,5),W); label("e",(0,4),W); label("d",(0,3),W);
+label("(A)",(-1,9),NW);
+draw((0,4)--(4,4),dashed); label("M",(4,4),E);
+draw((0,8)--(4,8),linewidth(1)); label("N",(4,8),E);
+draw((15,9)--(15,0)--(24,0));
+label("time",(19.5,0),S);
+label("s",(15,7),W); label("p",(15,6),W); label("e",(15,5),W); label("e",(15,4),W); label("d",(15,3),W);
+label("(B)",(14,9),NW);
+draw((15,4)--(19,4),dashed); label("M",(19,4),E);
+draw((15,8)--(23,8),linewidth(1)); label("N",(23,8),E);
+draw((30,9)--(30,0)--(39,0));
+label("time",(34.5,0),S);
+label("s",(30,7),W); label("p",(30,6),W); label("e",(30,5),W); label("e",(30,4),W); label("d",(30,3),W);
+label("(C)",(29,9),NW);
+draw((30,4)--(34,4),dashed); label("M",(34,4),E);
+draw((30,2)--(34,2),linewidth(1)); label("N",(34,2),E);
+draw((0,-6)--(0,-15)--(9,-15));
+label("time",(4.5,-15),S);
+label("s",(0,-8),W); label("p",(0,-9),W); label("e",(0,-10),W); label("e",(0,-11),W); label("d",(0,-12),W);
+label("(D)",(-1,-6),NW);
+draw((0,-11)--(4,-11),dashed); label("M",(4,-11),E);
+draw((0,-7)--(2,-7),linewidth(1)); label("N",(2,-7),E);
+draw((15,-6)--(15,-15)--(24,-15));
+label("time",(19.5,-15),S);
+label("s",(15,-8),W); label("p",(15,-9),W); label("e",(15,-10),W); label("e",(15,-11),W); label("d",(15,-12),W);
+label("(E)",(14,-6),NW);
+draw((15,-11)--(19,-11),dashed); label("M",(19,-11),E);
+draw((15,-13)--(23,-13),linewidth(1)); label("N",(23,-13),E);
+</asy>
+[[2001 AMC 8 Problems/Problem 19 | Solution]]
-[[AMC-8 2001 Problems/Problem 19 | Solution]]
 ==Problem 20==
+Kaleana shows her test score to Quay, Marty and Shana, but the others keep theirs hidden. Quay thinks, "At least two of us have the same score." Marty thinks, "I didn't get the lowest score." Shana thinks, "I didn't get the highest score." List the scores from lowest to highest for Marty (M), Quay (Q) and Shana (S).
+<math>\text{(A)}\ \text{S,Q,M} \qquad \text{(B)}\ \text{Q,M,S} \qquad \text{(C)}\ \text{Q,S,M} \qquad \text{(D)}\ \text{M,S,Q} \qquad \text{(E)}\ \text{S,M,Q}</math>
+[[2001 AMC 8 Problems/Problem 20 | Solution]]
-[[AMC-8 2001 Problems/Problem 20 | Solution]]
 ==Problem 21==
+The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest of these five integers is
+<math>\text{(A)}\ 19 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 35 \qquad \text{(E)}\ 40</math>
+[[2001 AMC 8 Problems/Problem 21 | Solution]]
-[[AMC-8 2001 Problems/Problem 21 | Solution]]
 ==Problem 22==
+On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and each incorrect answer is worth 0 points. Which of the following scores is '''NOT''' possible?
+<math>\text{(A)}\ 90 \qquad \text{(B)}\ 91 \qquad \text{(C)}\ 92 \qquad \text{(D)}\ 95 \qquad \text{(E)}\ 97</math>
+[[2001 AMC 8 Problems/Problem 22 | Solution]]
-[[AMC-8 2001 Problems/Problem 22 | Solution]]
 ==Problem 23==
+Points <math>R</math>, <math>S</math> and <math>T</math> are vertices of an equilateral triangle, and points <math>X</math>, <math>Y</math> and <math>Z</math> are midpoints of its sides. How many noncongruent triangles can be
+drawn using any three of these six points as vertices?
+<asy>
+pair SS,R,T,X,Y,Z;
+SS = (2,2*sqrt(3)); R = (0,0); T = (4,0);
+X = (2,0); Y = (1,sqrt(3)); Z = (3,sqrt(3));
+dot(SS); dot(R); dot(T); dot(X); dot(Y); dot(Z);
+label("$S$",SS,N); label("$R$",R,SW); label("$T$",T,SE);
+label("$X$",X,S); label("$Y$",Y,NW); label("$Z$",Z,NE);
+</asy>
+<math>\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 20</math>
+[[2001 AMC 8 Problems/Problem 23 | Solution]]
-[[AMC-8 2001 Problems/Problem 23 | Solution]]
 ==Problem 24==
+Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. There are 2 red-white pairs. How many white pairs coincide?
+<asy>
+draw((0,0)--(4,4*sqrt(3)));
+draw((1,-sqrt(3))--(5,3*sqrt(3)));
+draw((2,-2*sqrt(3))--(6,2*sqrt(3)));
+draw((3,-3*sqrt(3))--(7,sqrt(3)));
+draw((4,-4*sqrt(3))--(8,0));
+draw((8,0)--(4,4*sqrt(3)));
+draw((7,-sqrt(3))--(3,3*sqrt(3)));
+draw((6,-2*sqrt(3))--(2,2*sqrt(3)));
+draw((5,-3*sqrt(3))--(1,sqrt(3)));
+draw((4,-4*sqrt(3))--(0,0));
+draw((3,3*sqrt(3))--(5,3*sqrt(3)));
+draw((2,2*sqrt(3))--(6,2*sqrt(3)));
+draw((1,sqrt(3))--(7,sqrt(3)));
+draw((-1,0)--(9,0));
+draw((1,-sqrt(3))--(7,-sqrt(3)));
+draw((2,-2*sqrt(3))--(6,-2*sqrt(3)));
+draw((3,-3*sqrt(3))--(5,-3*sqrt(3)));
+</asy>
+<math>\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 9</math>
+[[2001 AMC 8 Problems/Problem 24 | Solution]]
-[[AMC-8 2001 Problems/Problem 24 | Solution]]
 ==Problem 25==
+There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly once. Only one of these four-digit numbers is a multiple of another one. Which of the following is it?
+<math>\text{(A)}\ 5724 \qquad \text{(B)}\ 7245 \qquad \text{(C)}\ 7254 \qquad \text{(D)}\ 7425 \qquad \text{(E)}\ 7542</math>
+[[2001 AMC 8 Problems/Problem 25 | Solution]]
+==See Also==
+{{AMC8 box|year=2001|before=[[2000 AMC 8 Problems|2000 AMC 8]]|after=[[2002 AMC 8 Problems|2002 AMC 8]]}}
+* [[AMC 8]]
+* [[AMC 8 Problems and Solutions]]
+* [[Mathematics competition resources]]
-[[AMC-8 2001 Problems/Problem 25 | Solution]]
+{{MAA Notice}}
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-* [[AMC-8 2001]]