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Difference between revisions of "2001 AMC 8 Problems"

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==Problem 1==
 
==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?
 
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?
  
−
<math> \mathrm{(A) \ 4 } \qquad \mathrm{(B) \ 6 } \qquad \mathrm{(C) \ 8 } \qquad \mathrm{(D) \ 10 } \qquad \mathrm{(E) \ 12 }  </math>
+
<math>\text{(A)}\ 4 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 12</math>
  
 
[[2001 AMC 8 Problems/Problem 1 | Solution]]
 
[[2001 AMC 8 Problems/Problem 1 | Solution]]
Line 8: Line 9:
 
==Problem 2==
 
==Problem 2==
  
 +
I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?
 +
 +
<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]]
 
[[2001 AMC 8 Problems/Problem 2 | Solution]]
 +
 
==Problem 3==
 
==Problem 3==
  
 +
Granny Smith has <dollar/>63. Elberta has <dollar/>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]]
 
[[2001 AMC 8 Problems/Problem 3 | Solution]]
 +
 
==Problem 4==
 
==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]]
 
[[2001 AMC 8 Problems/Problem 4 | Solution]]
 +
 
==Problem 5==
 
==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]]
 
[[2001 AMC 8 Problems/Problem 5 | Solution]]
 +
 
==Problem 6==
 
==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?
 +
 +
<math>\text{(A)}\ 90 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 105 \qquad \text{(D)}\ 120 \qquad \text{(E)}\ 140</math>
  
 
[[2001 AMC 8 Problems/Problem 6 | Solution]]
 
[[2001 AMC 8 Problems/Problem 6 | Solution]]
−
==Problem 7==
 
  
 +
==Kites on Parade==
 +
 +
''Problems 7, 8 and 9 are about these kites.''
 +
 +
<center>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. 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.</center>
 +
 +
{{image}}
 +
 +
===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]]
 
[[2001 AMC 8 Problems/Problem 7 | Solution]]
−
==Problem 8==
 
  
 +
===Problem 8===
 +
 +
Genevieve puts bracing on her large kite in the form of a 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]]
 
[[2001 AMC 8 Problems/Problem 8 | Solution]]
−
==Problem 9==
 
  
 +
===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]]
 
[[2001 AMC 8 Problems/Problem 9 | Solution]]
 +
 
==Problem 10==
 
==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]]
 
[[2001 AMC 8 Problems/Problem 10 | Solution]]
 +
 
==Problem 11==
 
==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
 +
 +
{{image}}
 +
 +
<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]]
 
[[2001 AMC 8 Problems/Problem 11 | Solution]]
 +
 
==Problem 12==
 
==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]]
 
[[2001 AMC 8 Problems/Problem 12 | Solution]]
 +
 
==Problem 13==
 
==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]]
 
[[2001 AMC 8 Problems/Problem 13 | Solution]]
 +
 
==Problem 14==
 
==Problem 14==
  

Revision as of 00:00, 13 May 2011

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?

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

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 <dollar/>63. Elberta has <dollar/>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

Kites on Parade

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. 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.

An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.

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 a 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

An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.

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

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

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

See Also

2001 AMC 8 (Problems • Answer Key • Resources)
Preceded by
2000 AMC 8 		Followed by
2002 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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