2000 AMC 8 Problems

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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?

$\mathrm{(A)}\ 15 \qquad \mathrm{(B)}\ 16 \qquad \mathrm{(C)}\ 17 \qquad \mathrm{(D)}\ 21 \qquad \mathrm{(E)}\ 37$

Solution

Problem 2

Which of these numbers is less than its reciprocal?

$\mathrm{(A)}\ -2 \qquad \mathrm{(B)}\ -1 \qquad \mathrm{(C)}\ 0 \qquad \mathrm{(D)}\ 1 \qquad \mathrm{(E)}\ 2$

Solution

Problem 3

How many whole numbers lie in the interval between $\frac{5}{3}$ and $2\pi?$


$\mathrm{(A)}\ 2 \qquad \mathrm{(B)}\ 3 \qquad \mathrm{(C)}\ 4 \qquad \mathrm{(D)}\ 5 \qquad \mathrm{(E)}$ infinitely many

Solution

Problem 4

In $1960$ only $5%$ (Error compiling LaTeX. ! Missing $ inserted.) of the working adults in Carlin City worked at home. By $1970$ the "at-home" work force had increased to $8%$ (Error compiling LaTeX. ! Missing $ inserted.). In $1980$ there were approximately $15%$ (Error compiling LaTeX. ! Missing $ inserted.) working at home, and in $1990$ there were $30%$ (Error compiling LaTeX. ! Missing $ inserted.). The graph that best illustrates this is:

$$ (Error compiling LaTeX. ! Missing $ inserted.)

Solution

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?

$\mathrm{(A)}\ 2 \qquad \mathrm{(B)}\ 3 \qquad \mathrm{(C)}\ 4 \qquad \mathrm{(D)}\ 5 \qquad \mathrm{(E)}\ 8$

Solution

Problem 6

Figure $ABCD$ 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

$\mathrm{(A)}\ 7 \qquad \mathrm{(B)}\ 10 \qquad \mathrm{(C)}\ 12.5 \qquad \mathrm{(D)}\ 14 \qquad \mathrm{(E)}\ 15$


Solution

Problem 7

What is the minimum possible product of three different numbers of the set ${-8.-6,-4,0,3,5,7}?$

$\mathrm{(A)}\ -336 \qquad \mathrm{(B)}\ -280 \qquad \mathrm{(C)}\ -210 \qquad \mathrm{(D)}\ -192 \qquad \mathrm{(E)}\ 0$

Solution

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 the view is

$\mathrm{(A)}\ 21 \qquad \mathrm{(B)}\ 22 \qquad \mathrm{(C)}\ 31 \qquad \mathrm{(D)}\ 41 \qquad \mathrm{(E)}\ 53$

Solution

Problem 9

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