View source

==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)}\ 15
\qquad
\mathrm{(B)}\ 16
\qquad
\mathrm{(C)}\ 17
\qquad
\mathrm{(D)}\ 21
\qquad
\mathrm{(E)}\ 37
</math>

[[2000 AMC 8 Problems/Problem 1|Solution]]

==Problem 2==
Which of these numbers is less than its reciprocal?

<math>
\mathrm{(A)}\ -2
\qquad
\mathrm{(B)}\ -1
\qquad
\mathrm{(C)}\ 0
\qquad
\mathrm{(D)}\ 1
\qquad
\mathrm{(E)}\ 2
</math>

[[2000 AMC 8 Problems/Problem 2|Solution]]

==Problem 3==
How many whole numbers lie in the interval between <math>\frac{5}{3}</math> and <math>2\pi?</math>


<math>
\mathrm{(A)}\ 2
\qquad
\mathrm{(B)}\ 3
\qquad
\mathrm{(C)}\ 4
\qquad
\mathrm{(D)}\ 5
\qquad
\mathrm{(E)}\ infinitely\ many
</math>

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

==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:

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

==Problem 5==
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>
\mathrm{(A)}\ 2
\qquad
\mathrm{(B)}\ 3
\qquad
\mathrm{(C)}\ 4
\qquad
\mathrm{(D)}\ 5
\qquad
\mathrm{(E)}\ 8
</math>

[[2000 AMC 8 Problems/Problem 5|Solution]]

==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 <math>L</math>-shaped region is

<math>
\mathrm{(A)}\ 7
\qquad
\mathrm{(B)}\ 10
\qquad
\mathrm{(C)}\ 12.5
\qquad
\mathrm{(D)}\ 14
\qquad
\mathrm{(E)}\ 15
</math>


[[2000 AMC 8 Problems/Problem 6|Solution]]

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

<math>
\mathrm{(A)}\ -336
\qquad
\mathrm{(B)}\ -280
\qquad
\mathrm{(C)}\ -210
\qquad
\mathrm{(D)}\ -192
\qquad
\mathrm{(E)}\ 0
</math>

[[2000 AMC 8 Problems/Problem 7|Solution]]

==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 this view is

<math>
\mathrm{(A)}\ 21
\qquad
\mathrm{(B)}\ 22
\qquad
\mathrm{(C)}\ 31
\qquad
\mathrm{(D)}\ 41
\qquad
\mathrm{(E)}\ 53
</math>

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

==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]]

==Problem 17==
==Problem 18==
==Problem 19==
==Problem 20==
==Problem 21==
==Problem 22==
==Problem 23==
==Problem 24==
==Problem 25==