1985 AMC 8

What is the value of the following product?

$$
\dfrac{3 \times 5}{9 \times 11} \times \dfrac{7 \times 9 \times 11}{3 \times 5 \times 7}
$$

What is the value of $90 + 91 + 92 + \cdots + 98 + 99?$

What is the value of the following expression?

$$
\dfrac{10^7}{5 \times 10^4}
$$

The area of polygon $ABCDEF,$ in square units, is

The grades in a mathematics class for the last grading period were: $5$ students earned an A, $4$ earned a B, $3$ earned a C, $3$ earned a D, and $5$ earned an F. If A, B, C, and D are satisfactory grades, what fraction of the grades are satisfactory?

A ream of paper containing $500$ sheets is $5$ cm thick. Approximately how many sheets of this type of paper would there be in a stack $7.5$ cm high?

A “stair-step” figure is made up of alternating shaded and unshaded squares in each row. Rows $1$ through $4$ are shown. All rows begin and end with an unshaded square. The number of shaded squares in the $37$th row is

If $a = -2,$ the largest number in the set

$$
\left\{ -3a,\ 4a,\ \dfrac{24}{a},\ a^2,\ 1 \right\}
$$

is

What is the value of the product of the $9$ factors below?

$$
\begin{aligned} &\left(1 - \tfrac12\right)\left(1 - \tfrac13\right)\left(1 - \tfrac14\right) \cdots \\ &\quad {}\cdot \left(1 - \tfrac{1}{10}\right) \end{aligned}
$$

What fraction lies halfway between $\dfrac15$ and $\dfrac13$ on the number line?

A piece of paper containing six joined squares labeled as shown is folded along the edges of the squares to form a cube. The label of the face opposite the face labeled $X$ is

A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are $6.2$ cm, $8.3$ cm, and $9.5$ cm. The area of the square, in square centimeters, is

If you walk for $45$ minutes at a rate of $4$ mph and then run for $30$ minutes at a rate of $10$ mph, how many miles have you gone at the end of one hour and $15$ minutes?

The difference between a $6.5\%$ sales tax and a $6\%$ sales tax on an item priced at $\$20$ before tax is

How many whole numbers between $100$ and $400$ contain the digit $2?$

The ratio of boys to girls in Mr. Brown’s math class is $2 : 3.$ If there are $30$ students in the class, how many more girls than boys are in the class?

If your average score on your first six mathematics tests was $84$ and your average score on your first seven mathematics tests was $85,$ then your score on the seventh test was

Nine copies of a certain pamphlet cost less than $\$10.00$ while ten copies of the same pamphlet (at the same price) cost more than $\$11.00.$ How much does one copy of this pamphlet cost?

If the length and width of a rectangle are each increased by $10\%,$ then the perimeter of the rectangle is increased by

In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January $1$ fall that year?