This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 10

1985 AMC 8, 3

$ \frac{10^7}{5 \times 10^4}\equal{}$ \[ \textbf{(A)}\ .002 \qquad \textbf{(B)}\ .2 \qquad \textbf{(C)}\ 20 \qquad \textbf{(D)}\ 200 \qquad \textbf{(E)}\ 2000 \]

1985 AMC 8, 12

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 is \[ \textbf{(A)}\ 24 \text{ cm}^2 \qquad \textbf{(B)}\ 36 \text{ cm}^2 \qquad \textbf{(C)}\ 48 \text{ cm}^2 \qquad \textbf{(D)}\ 64 \text{ cm}^2 \qquad \textbf{(E)}\ 144 \text{ cm}^2 \]

1985 AMC 8, 17

Tags: Why the bump
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 \[ \textbf{(A)}\ 86 \qquad \textbf{(B)}\ 88 \qquad \textbf{(C)}\ 90 \qquad \textbf{(D)}\ 91 \qquad \textbf{(E)}\ 92 \]

1985 AMC 8, 5

Tags: Why the bump
[asy]size(180); draw((1,0)--(2,0)--(2,10)--(1,10)--cycle); draw((3,0)--(4,0)--(4,8)--(3,8)--cycle); draw((5,0)--(6,0)--(6,6)--(5,6)--cycle); draw((7,0)--(8,0)--(8,6)--(7,6)--cycle); draw((9,0)--(10,0)--(10,10)--(9,10)--cycle); draw((0,2)--(-0.5,2)); draw((0,4)--(-0.5,4)); draw((0,6)--(-0.5,6)); draw((0,8)--(-0.5,8)); draw((0,10)--(-0.5,10)); draw((0,10)--(0,0)); draw((0,0)--(10,0)); label("1",(-0.5,2),W); label("2",(-0.5,4),W); label("3",(-0.5,6),W); label("4",(-0.5,8),W); label("5",(-0.5,10),W); label("A",(1.5,-0.5),S); label("B",(3.5,-0.5),S); label("C",(5.5,-0.5),S); label("D",(7.5,-0.5),S); label("F",(9.5,-0.5),S); label("Grade",(5,-3),S); label("$\#$ of Students",(-4,5),W);[/asy] The bar graph shows the grades in a mathematics class for the last grading period. If A, B, C, and D are satisfactory grades, what fraction of the grades shown in the graph are satisfactory? \[ \textbf{(A)}\ \frac{1}{2} \qquad \textbf{(B)}\ \frac{2}{3} \qquad \textbf{(C)}\ \frac{3}{4} \qquad \textbf{(D)}\ \frac{4}{5} \qquad \textbf{(E)}\ \frac{9}{10} \]

1985 AMC 8, 15

Tags: Why the bump
How many whole numbers between $ 100$ and $ 400$ contain the digit $ 2$? \[ \textbf{(A)}\ 100 \qquad \textbf{(B)}\ 120 \qquad \textbf{(C)}\ 138 \qquad \textbf{(D)}\ 140 \qquad \textbf{(E)}\ 148 \]

1985 AMC 8, 16

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? \[ \textbf{(A)}\ 1 \qquad \textbf{(B)}\ 3 \qquad \textbf{(C)}\ 5 \qquad \textbf{(D)}\ 6 \qquad \textbf{(E)}\ 10 \]

1985 AMC 8, 4

The area of polygon $ ABCDEF$, in square units, is [asy]draw((0,0)--(4,0)--(4,9)--(-2,9)--(-2,4)--(0,4)--cycle); label("A",(-2,9),NW); label("B",(4,9),NE); label("C",(4,0),SE); label("D",(0,0),SW); label("E",(0,4),NE); label("F",(-2,4),SW); label("5",(-2,6.5),W); label("4",(2,0),S); label("9",(4,4.5),E); label("6",(1,9),N); label("All angles in this diagram are right.",(0,-3),S);[/asy] \[ \textbf{(A)}\ 24 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 46 \qquad \textbf{(D)}\ 66 \qquad \textbf{(E)}\ 74 \]

1985 AMC 8, 22

Assume every $ 7$-digit whole number is a possible telephone number except those which begin with $ 0$ or $ 1$. What fraction of telephone numbers begin with $ 9$ and end with $ 0$? \[ \textbf{(A)}\ \frac{1}{63} \qquad \textbf{(B)}\ \frac{1}{80} \qquad \textbf{(C)}\ \frac{1}{81} \qquad \textbf{(D)}\ \frac{1}{90} \qquad \textbf{(E)}\ \frac{1}{100} \]

1985 AMC 8, 13

Tags: Why the bump
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? \[ \textbf{(A)}\ 3.5 \text{ miles} \qquad \textbf{(B)}\ 8 \text{ miles} \qquad \textbf{(C)}\ 9 \text{ miles} \qquad \textbf{(D)}\ 25 \frac{1}{3} \text{ miles} \qquad \textbf{(E)}\ 480 \text{ miles} \]

1985 AMC 8, 18

Tags: Why the bump
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? \[ \textbf{(A)}\ \$1.07 \qquad \textbf{(B)}\ \$1.08 \qquad \textbf{(C)}\ \$1.09 \qquad \textbf{(D)}\ \$1.10 \qquad \textbf{(E)}\ \$1.11 \]