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?

$\mathrm{(A)}\ 40\qquad\mathrm{(B)}\ 200\qquad\mathrm{(C)}\ 400\qquad\mathrm{(D)}\ 500\qquad\mathrm{(E)}\ 1000$

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2000 AMC 8

From AoPSWiki

Contents

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25