ΒΆ 1990 AMC8 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 1990 AMC8 problems here.
Discussion Forum
Engage in discussion about the 1990 AMC8 math contest by visiting Random Math 1990 AMC8 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 1990 AMC8 problems, please refer below:
Problem 1: What is the smallest sum of two -digit numbers that can be obtained by placing each of the six digits in one of the six boxes in this addition problem?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 2: Which digit of , when changed to , gives the largest number?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 3: What fraction of the square is shaded?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 4: Which of the following could not be the unit's digit [one's digit] of the square of a whole number?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 5: Which of the following is closest to the product
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 6: Which of these five numbers is the largest?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 7: When three different numbers from the set are multiplied, the largest possible product is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 8: A dress originally priced at was put on sale at off. If tax was added to the sale price, then the total selling price of the dress was
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 9: The grading scale shown is used at Jones Junior High. The fifteen scores in Mr. Freeman's class were:
In Mr. Freeman's class, what percent of the students received a grade of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 10: On this monthly calendar, the date behind one of the letters is added to the date behind . If this sum equals the sum of the dates behind and , then the letter is:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 11: The numbers on the faces of this cube are consecutive whole numbers. The sums of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 12: There are twenty-four -digit whole numbers that use each of the four digits , and exactly once. Listed in numerical order from smallest to largest, the number in the th position in the list is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 13: One proposal for new postage rates for a letter was for the first ounce and for each additional ounce (or fraction of an ounce). The postage for a letter weighing ounces was
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 14: A bag contains only blue balls and green balls. There are blue balls. If the probability of drawing a blue ball at random from this bag is , then the number of green balls in the bag is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 15: The area of this figure is . Its perimeter is
.jpg)
[figure consists of four identical squares]
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 16:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 17: A straight concrete sidewalk is to be feet wide, feet long and inches thick. How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of cubic yards?
Answer Choices:
A.
B.
C.
D.
E. more than
Solution:
Problem 18: Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 19: There are seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 20: The annual incomes of families range from to . In error, the largest income was entered on the computer as . The difference between the mean of the incorrect data and the mean of the actual data is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 21: A list of numbers is formed by beginning with two given numbers. Each new number in the list is the product of the two previous numbers. Find the first number if the last three are shown:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 22: Several students are seated at a large circular table. They pass around a bag containing pieces of candy. Each person receives the bag, takes one piece of candy and then passes the bag to the next person. If Chris takes the first and the last piece of candy, then the number of students at the table could be
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 23: The graph relates the distance traveled [in miles] to the time elapsed [in hours] on a trip taken by an experimental airplane. During which hour was the average speed of this airplane the largest?
.jpg)
Answer Choices:
A. first
B. second
C. third
D. ninth
E. last
Solution:
Problem 24: Three 's and a will balance nine 's. One will balance a and a .
.jpg)
How many 's will balance the two 's in this balance?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 25: Three 's and a will balance nine 's. One will balance a and a .
How many 's will balance the two 's in this balance?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions