Difference between revisions of "1990 AJHSME Problems"
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==Problem 1== | ==Problem 1== | ||
Latest revision as of 15:03, 6 October 2021
1990 AJHSME (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 |
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
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?
Problem 2
Which digit of , when changed to , gives the largest number?
Problem 3
What fraction of the square is shaded?
Problem 4
Which of the following could not be the unit's digit [one's digit] of the square of a whole number?
Problem 5
Which of the following is closest to the product ?
Problem 6
Which of these five numbers is the largest?
Problem 7
When three different numbers from the set are multiplied, the largest possible product is
Problem 8
A dress originally priced at dollars was put on sale for off. If tax was added to the sale price, then the total selling price (in dollars) of the dress was
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 C?
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
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
Problem 12
There are twenty-four -digit numbers that use each of the four digits , , , and exactly once. Listed in numerical order from smallest to largest, the number in the position in the list is
Problem 13
One proposal for new postage rates for a letter was cents for the first ounce and cents for each additional ounce (or fraction of an ounce). The postage for a letter weighing ounces was
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
Problem 15
The area of this figure is . Its perimeter is
Problem 16
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?
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?
Assume that the planes cutting the prism do not intersect anywhere in or on the prism.
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?
Problem 20
The annual incomes of families range from dollars to dollars. In error, the largest income was entered on the computer as dollars. The difference between the mean of the incorrect data and the mean of the actual data is
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:
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 last piece of candy, then the number of students at the table could be
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?
Problem 24
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?
Problem 25
How many different patterns can be made by shading exactly two of the nine squares? Patterns that can be matched by flips and/or turns are not considered different. For example, the patterns shown below are not considered different.
See also
1990 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by 1989 AJHSME |
Followed by 1991 AJHSME | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.