# Difference between revisions of "2000 AMC 8 Problems"

(New page: ==Problem 1== Aunt Anna is <math>42</math> years old. Caitlin is <math>5</math> years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin? <math> \mathrm{(A)...) |
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Line 46: | Line 46: | ||

\mathrm{(D)}\ 5 | \mathrm{(D)}\ 5 | ||

\qquad | \qquad | ||

− | \mathrm{(E)}</math> | + | \mathrm{(E)}\ infinitely\ many |

+ | </math> | ||

[[2000 AMC 8 Problems/Problem 3|Solution]] | [[2000 AMC 8 Problems/Problem 3|Solution]] | ||

==Problem 4== | ==Problem 4== | ||

− | In <math>1960</math> only <math>5%</math> of the working adults in Carlin City worked at home. By <math>1970</math> the "at-home" work force had increased to <math>8%</math>. In <math>1980</math> there were approximately <math>15%</math> working at home, and in <math>1990</math> there were <math>30%</math>. The graph that best illustrates this is: | + | In <math>1960</math> only <math>5\%</math> of the working adults in Carlin City worked at home. By <math>1970</math> the "at-home" work force had increased to <math>8\%</math>. In <math>1980</math> there were approximately <math>15\%</math> working at home, and in <math>1990</math> there were <math>30\%</math>. The graph that best illustrates this is: |

− | |||

− | |||

− | |||

[[2000 AMC 8 Problems/Problem 4|Solution]] | [[2000 AMC 8 Problems/Problem 4|Solution]] | ||

==Problem 5== | ==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? | + | Each principal of Lincoln High School serves exactly one <math>3</math>-year term. What is the maximum number of principals this school could have during an <math>8</math>-year period? |

<math> | <math> | ||

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==Problem 6== | ==Problem 6== | ||

− | 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 | + | 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 <math>L</math>-shaped region is |

<math> | <math> | ||

Line 94: | Line 92: | ||

==Problem 7== | ==Problem 7== | ||

− | What is the minimum possible product of three different numbers of the set <math>{-8.-6,-4,0,3,5,7}?</math> | + | What is the minimum possible product of three different numbers of the set <math>\{-8.-6,-4,0,3,5,7\}?</math> |

<math> | <math> | ||

Line 111: | Line 109: | ||

==Problem 8== | ==Problem 8== | ||

− | Three dice with faces numbered <math>1</math> through <math>6</math> are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots <math>NOT</math> visible in | + | Three dice with faces numbered <math>1</math> through <math>6</math> are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots <math>NOT</math> visible in this view is |

<math> | <math> | ||

Line 125: | Line 123: | ||

</math> | </math> | ||

− | [[2000 AMC 8 Problems/Problem | + | [[2000 AMC 8 Problems/Problem 8|Solution]] |

==Problem 9== | ==Problem 9== | ||

+ | Three-digit powers of <math>2</math> and <math>5</math> are used in this <math>cross-number</math> puzzle. What is the only possible digit for the outlined square? | ||

+ | |||

+ | <math>ACROSS\ DOWN</math> | ||

+ | |||

+ | <math>2)\ 2^m \qquad\ 1)\ 5^n</math> | ||

+ | |||

+ | |||

+ | <math> | ||

+ | \mathrm{(A)}\ 0 | ||

+ | \qquad | ||

+ | \mathrm{(B)}\ 2 | ||

+ | \qquad | ||

+ | \mathrm{(C)}\ 4 | ||

+ | \qquad | ||

+ | \mathrm{(D)}\ 6 | ||

+ | \qquad | ||

+ | \mathrm{(E)}\ 8 | ||

+ | </math> | ||

+ | |||

+ | [[2000 AMC 8 Problems/Problem 9|Solution]] | ||

+ | |||

+ | ==Problem 10== | ||

+ | Ara and Shea were once the same height. Since then Shea has grown <math>20\%</math> while Ara has grow half as many inches as Shea. Shea is now <math>60</math> inches tall. How tall, in inches, is Ara now? | ||

+ | |||

+ | <math> | ||

+ | \mathrm{(A)}\ 48 | ||

+ | \qquad | ||

+ | \mathrm{(B)}\ 51 | ||

+ | \qquad | ||

+ | \mathrm{(C)}\ 52 | ||

+ | \qquad | ||

+ | \mathrm{(D)}\ 54 | ||

+ | \qquad | ||

+ | \mathrm{(E)}\ 55 | ||

+ | </math> | ||

+ | |||

+ | [[2000 AMC 8 Problems/Problem 10|Solution]] | ||

+ | |||

+ | ==Problem 11== | ||

+ | The number <math>64</math> has the property that it is divisible by its units digit. How many whole numbers between <math>10</math> and <math>50</math> have this property? | ||

+ | |||

+ | |||

+ | <math> | ||

+ | \mathrm{(A)}\ 15 | ||

+ | \qquad | ||

+ | \mathrm{(B)}\ 16 | ||

+ | \qquad | ||

+ | \mathrm{(C)}\ 17 | ||

+ | \qquad | ||

+ | \mathrm{(D)}\ 18 | ||

+ | \qquad | ||

+ | \mathrm{(E)}\ 20 | ||

+ | </math> | ||

+ | |||

+ | [[2000 AMC 8 Problems/Problem 11|Solution]] | ||

+ | |||

+ | ==Problem 12== | ||

+ | ==Problem 13== | ||

+ | ==Problem 14== | ||

+ | What is the units digit of <math>19^{19} + 99^{99}?</math> | ||

+ | |||

+ | <math> | ||

+ | \mathrm{(A)}\ 0 | ||

+ | \qquad | ||

+ | \mathrm{(B)}\ 1 | ||

+ | \qquad | ||

+ | \mathrm{(C)}\ 2 | ||

+ | \qquad | ||

+ | \mathrm{(D)}\ 8 | ||

+ | \qquad | ||

+ | \mathrm{(E)}\ 9 | ||

+ | </math> | ||

+ | |||

+ | [[2000 AMC 8 Problems/Problem 14|Solution]] | ||

+ | |||

+ | ==Problem 15== | ||

+ | ==Problem 16== | ||

+ | In order for Mateen to walk a kilometer <math>(1000m)</math> in his rectangular backyard, he must walk the length <math>25</math> times or walk its perimeter <math>10</math> times. What is the area of Mateen's backyard in square meters? | ||

+ | |||

+ | <math> | ||

+ | \mathrm{(A)}\ 40 | ||

+ | \qquad | ||

+ | \mathrm{(B)}\ 200 | ||

+ | \qquad | ||

+ | \mathrm{(C)}\ 400 | ||

+ | \qquad | ||

+ | \mathrm{(D)}\ 500 | ||

+ | \qquad | ||

+ | \mathrm{(E)}\ 1000 | ||

+ | </math> | ||

+ | |||

+ | [[2000 AMC 8 Problems/Problem 16|Solution]] |

## Revision as of 09:37, 10 April 2009

## Contents

## Problem 1

Aunt Anna is years old. Caitlin is 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

In only of the working adults in Carlin City worked at home. By the "at-home" work force had increased to . In there were approximately working at home, and in there were . The graph that best illustrates this is:

## Problem 5

Each principal of Lincoln High School serves exactly one -year term. What is the maximum number of principals this school could have during an -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 -shaped region is

## Problem 7

What is the minimum possible product of three different numbers of the set

## Problem 8

Three dice with faces numbered through are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots visible in this view is

## Problem 9

Three-digit powers of and are used in this puzzle. What is the only possible digit for the outlined square?

## Problem 10

Ara and Shea were once the same height. Since then Shea has grown while Ara has grow half as many inches as Shea. Shea is now inches tall. How tall, in inches, is Ara now?

## Problem 11

The number has the property that it is divisible by its units digit. How many whole numbers between and 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 in his rectangular backyard, he must walk the length times or walk its perimeter times. What is the area of Mateen's backyard in square meters?