2000 AMC 8

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

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 this view is

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

Solution

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?

$ACROSS\ DOWN$

$2)\ 2^m \qquad\ 1)\ 5^n$

$\mathrm{(A)}\ 0\qquad\mathrm{(B)}\ 2\qquad\mathrm{(C)}\ 4\qquad\mathrm{(D)}\ 6\qquad\mathrm{(E)}\ 8$

Solution

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?

$\mathrm{(A)}\ 48\qquad\mathrm{(B)}\ 51\qquad\mathrm{(C)}\ 52\qquad\mathrm{(D)}\ 54\qquad\mathrm{(E)}\ 55$

Solution

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?

$\mathrm{(A)}\ 15\qquad\mathrm{(B)}\ 16\qquad\mathrm{(C)}\ 17\qquad\mathrm{(D)}\ 18\qquad\mathrm{(E)}\ 20$

Solution

Problem 12

Problem 13

Problem 14

What is the units digit of $19^{19} + 99^{99}?$

$\mathrm{(A)}\ 0\qquad\mathrm{(B)}\ 1\qquad\mathrm{(C)}\ 2\qquad\mathrm{(D)}\ 8\qquad\mathrm{(E)}\ 9$

Solution

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?