ONLINE AMC 8 PREP WITH AOPS
Difference between revisions of "2000 AMC 8 Problems"
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==Problem 1== | ==Problem 1== | ||
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| − | <math> | + | Aunt Anna is 42 years old. Caitlin is 5 years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin? |
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| − | \qquad | + | <math>\text{(A)}\ 15 \qquad \text{(B)}\ 16 \qquad \text{(C)}\ 17 \qquad \text{(D)}\ 21 \qquad \text{(E)}\ 37</math> |
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[[2000 AMC 8 Problems/Problem 1|Solution]] | [[2000 AMC 8 Problems/Problem 1|Solution]] | ||
| − | ==Problem 2== | + | == Problem 2 == |
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Which of these numbers is less than its reciprocal? | Which of these numbers is less than its reciprocal? | ||
| − | <math> | + | <math>\text{(A)}\ -2 \qquad \text{(B)}\ -1 \qquad \text{(C)}\ 0 \qquad \text{(D)}\ 1 \qquad \text{(E)}\ 2</math> |
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| − | </math> | ||
[[2000 AMC 8 Problems/Problem 2|Solution]] | [[2000 AMC 8 Problems/Problem 2|Solution]] | ||
==Problem 3== | ==Problem 3== | ||
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How many whole numbers lie in the interval between <math>\frac{5}{3}</math> and <math>2\pi?</math> | How many whole numbers lie in the interval between <math>\frac{5}{3}</math> and <math>2\pi?</math> | ||
| − | + | <math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ \text{infinitely many}</math> | |
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| − | </math> | ||
[[2000 AMC 8 Problems/Problem 3|Solution]] | [[2000 AMC 8 Problems/Problem 3|Solution]] | ||
==Problem 4== | ==Problem 4== | ||
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[[2000 AMC 8 Problems/Problem 4|Solution]] | [[2000 AMC 8 Problems/Problem 4|Solution]] | ||
==Problem 5== | ==Problem 5== | ||
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| − | <math> | + | Each principal of Lincoln High School serves exactly one 3-year term. What is the maximum number of principals this school could have during an 8-year period? |
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| − | \qquad | + | <math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 8</math> |
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| − | </math> | ||
[[2000 AMC 8 Problems/Problem 5|Solution]] | [[2000 AMC 8 Problems/Problem 5|Solution]] | ||
==Problem 6== | ==Problem 6== | ||
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| − | <math> | + | Figure <math>ABCD</math> is a square. Inside this square three smaller squares are drawn with the side lengths as labeled. The area of the shaded L-shaped region is |
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| + | <math>\text{(A)}\ 7 \qquad \text{(B)}\ 10 \qquad \text{(C)}\ 12.5 \qquad \text{(D)}\ 14 \qquad \text{(E)}\ 15</math> | ||
[[2000 AMC 8 Problems/Problem 6|Solution]] | [[2000 AMC 8 Problems/Problem 6|Solution]] | ||
==Problem 7== | ==Problem 7== | ||
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| − | <math> | + | What is the minimum possible product of three different numbers of the set <math>\{-8,-6,-4,0,3,5,7\}</math>? |
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| − | \qquad | + | <math>\text{(A)}\ -336 \qquad \text{(B)}\ -280 \qquad \text{(C)}\ -210 \qquad \text{(D)}\ -192 \qquad \text{(E)}\ 0</math> |
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| − | </math> | ||
[[2000 AMC 8 Problems/Problem 7|Solution]] | [[2000 AMC 8 Problems/Problem 7|Solution]] | ||
==Problem 8== | ==Problem 8== | ||
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| − | <math> | + | Three dice with faces numbered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots NOT visible in this view is |
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| − | \qquad | + | {{image}} |
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| − | \qquad | + | <math>\text{(A)}\ 21 \qquad \text{(B)}\ 22 \qquad \text{(C)}\ 31 \qquad \text{(D)}\ 41 \qquad \text{(E)}\ 53</math> |
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| − | </math> | ||
[[2000 AMC 8 Problems/Problem 8|Solution]] | [[2000 AMC 8 Problems/Problem 8|Solution]] | ||
==Problem 9== | ==Problem 9== | ||
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| − | + | Three-digit powers of 2 and 5 are used in this ''cross-number'' puzzle. What is the only possible digit for the outlined square? | |
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| − | + | <math>\text{(A)}\ 0 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math> | |
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| − | </math> | ||
[[2000 AMC 8 Problems/Problem 9|Solution]] | [[2000 AMC 8 Problems/Problem 9|Solution]] | ||
==Problem 10== | ==Problem 10== | ||
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| − | <math> | + | Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grow half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now? |
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| − | \qquad | + | <math>\text{(A)}\ 48 \qquad \text{(B)}\ 51 \qquad \text{(C)}\ 52 \qquad \text{(D)}\ 54 \qquad \text{(E)}\ 55</math> |
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[[2000 AMC 8 Problems/Problem 10|Solution]] | [[2000 AMC 8 Problems/Problem 10|Solution]] | ||
==Problem 11== | ==Problem 11== | ||
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| + | The number 64 has the property that it is divisible by its units digit. How many whole numbers between 10 and 50 have this property? | ||
| − | <math> | + | <math>\text{(A)}\ 15 \qquad \text{(B)}\ 16 \qquad \text{(C)}\ 17 \qquad \text{(D)}\ 18 \qquad \text{(E)}\ 20</math> |
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[[2000 AMC 8 Problems/Problem 11|Solution]] | [[2000 AMC 8 Problems/Problem 11|Solution]] | ||
==Problem 12== | ==Problem 12== | ||
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| + | [[2000 AMC 8 Problems/Problem 12|Solution]] | ||
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==Problem 13== | ==Problem 13== | ||
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| + | [[2000 AMC 8 Problems/Problem 13|Solution]] | ||
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==Problem 14== | ==Problem 14== | ||
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| − | <math> | + | What is the units digit of <math>19^{19} + 99^{99}</math>? |
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| − | \qquad | + | <math>\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 9</math> |
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| − | </math> | ||
[[2000 AMC 8 Problems/Problem 14|Solution]] | [[2000 AMC 8 Problems/Problem 14|Solution]] | ||
==Problem 15== | ==Problem 15== | ||
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| + | [[2000 AMC 8 Problems/Problem 15|Solution]] | ||
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==Problem 16== | ==Problem 16== | ||
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| − | <math> | + | In order for Mateen to walk a kilometer (1000m) in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters? |
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| − | \qquad | + | <math>\text{(A)}\ 40 \qquad \text{(B)}\ 200 \qquad \text{(C)}\ 400 \qquad \text{(D)}\ 500 \qquad \text{(E)}\ 1000</math> |
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| − | </math> | ||
[[2000 AMC 8 Problems/Problem 16|Solution]] | [[2000 AMC 8 Problems/Problem 16|Solution]] | ||
==Problem 17== | ==Problem 17== | ||
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| + | [[2000 AMC 8 Problems/Problem 17|Solution]] | ||
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==Problem 18== | ==Problem 18== | ||
| − | ==Problem 19== | + | |
| + | [[2000 AMC 8 Problems/Problem 18|Solution]] | ||
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| + | ===Problem 19=== | ||
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| + | [[2000 AMC 8 Problems/Problem 19|Solution]] | ||
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==Problem 20== | ==Problem 20== | ||
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| + | [[2000 AMC 8 Problems/Problem 20|Solution]] | ||
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==Problem 21== | ==Problem 21== | ||
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| + | [[2000 AMC 8 Problems/Problem 21|Solution]] | ||
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==Problem 22== | ==Problem 22== | ||
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| + | [[2000 AMC 8 Problems/Problem 22|Solution]] | ||
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==Problem 23== | ==Problem 23== | ||
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| + | [[2000 AMC 8 Problems/Problem 23|Solution]] | ||
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==Problem 24== | ==Problem 24== | ||
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| + | [[2000 AMC 8 Problems/Problem 24|Solution]] | ||
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==Problem 25== | ==Problem 25== | ||
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| + | [[2000 AMC 8 Problems/Problem 25|Solution]] | ||
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| + | == See also == | ||
| + | {{AMC8 box|year=2000|before=[[1999 AMC 8 Problems|1998 AMC 8]]|after=[[2001 AMC 8 Problems|2001 AMC 8]]}} | ||
| + | * [[AMC 8]] | ||
| + | * [[AMC 8 Problems and Solutions]] | ||
| + | * [[Mathematics competition resources]] | ||
Revision as of 14:21, 24 April 2011
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 20
- 20 Problem 21
- 21 Problem 22
- 22 Problem 23
- 23 Problem 24
- 24 Problem 25
- 25 See also
Problem 1
Aunt Anna is 42 years old. Caitlin is 5 years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin?
Problem 2
Which of these numbers is less than its reciprocal?
Problem 3
How many whole numbers lie in the interval between 
and 
Problem 4
Problem 5
Each principal of Lincoln High School serves exactly one 3-year term. What is the maximum number of principals this school could have during an 8-year period?
Problem 6
Figure 
is a square. Inside this square three smaller squares are drawn with the side lengths as labeled. The area of the shaded L-shaped region is
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 minimum possible product of three different numbers of the set 
?
Problem 8
Three dice with faces numbered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots NOT visible in this view is
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
Problem 9
Three-digit powers of 2 and 5 are used in this cross-number puzzle. What is the only possible digit for the outlined square?
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
Problem 10
Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grow half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now?
Problem 11
The number 64 has the property that it is divisible by its units digit. How many whole numbers between 10 and 50 have this property?
Problem 12
Problem 13
Problem 14
What is the units digit of 
?
Problem 15
Problem 16
In order for Mateen to walk a kilometer (1000m) in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters?
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
See also
| 2000 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by 1998 AMC 8 |
Followed by 2001 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 | ||
