Difference between revisions of "1994 AJHSME Problems"
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A gumball machine contains <math>9</math> red, <math>7</math> white, and <math>8</math> blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is | A gumball machine contains <math>9</math> red, <math>7</math> white, and <math>8</math> blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is | ||
− | <math>\text{(A)}\ 8 \qquad \text{(B)}\ 9 \qquad \text(C)}\ 10 \qquad \text{(D)}\ 12 \qquad \text{(E)}\ 18</math> | + | <math>\text{(A)}\ 8 \qquad \text{(B)}\ 9 \qquad \text{(C)}\ 10 \qquad \text{(D)}\ 12 \qquad \text{(E)}\ 18</math> |
[[1994 AJHSME Problems/Problem 21|Solution]] | [[1994 AJHSME Problems/Problem 21|Solution]] |
Revision as of 19:39, 10 March 2015
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
Which of the following is the largest?
Problem 2
Problem 3
Each day Maria must work hours. This does not include the minutes she takes for lunch. If she begins working at and takes her lunch break at noon, then her working day will end at
Problem 4
Which of the following represents the result when the figure shown below is rotated clockwise around its center?
Problem 5
Given that and , the number of rods in one mile is
Problem 6
The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is
Problem 7
If , and , then
Problem 8
For how many three-digit whole numbers does the sum of the digits equal ?
Problem 9
A shopper buys a dollar coat on sale for off. An additional dollars are taken off the sale price by using a discount coupon. A sales tax of is paid on the final selling price. The total amount the shopper pays for the coat is
Problem 10
For how many positive integer values of is the expression an integer?
Problem 11
Last summer students attended basketball camp. Of those attending, were boys and were girls. Also, students were from Jonas Middle School and were from Clay Middle School. Twenty of the girls were from Jonas Middle School. How many of the boys were from Clay Middle School?
Problem 12
Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare?
Problem 13
The number halfway between and is
Problem 14
Two children at a time can play pairball. For minutes, with only two children playing at time, five children take turns so that each one plays the same amount of time. The number of minutes each child plays is
Problem 15
If this path is to continue in the same pattern:
then which sequence of arrows goes from point to point ?
Problem 16
The perimeter of one square is times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?
Problem 17
Pauline Bunyan can shovel snow at the rate of cubic yards for the first hour, cubic yards for the second, for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is yards wide, yards long, and covered with snow yards deep, then the number of hours it will take her to shovel it clean is closest to
Problem 18
Mike leaves home and drives slowly east through city traffic. When he reaches the highway he drives east more rapidly until he reaches the shopping mall where he stops. He shops at the mall for an hour. Mike returns home by the same route as he came, driving west rapidly along the highway and then slowly through city traffic. Each graph shows the distance from home on the vertical axis versus the time elapsed since leaving home on the horizontal axis. Which graph is the best representation of Mike's trip?
Problem 19
Around the outside of a by square, construct four semicircles (as shown in the figure) with the four sides of the square as their diameters. Another square, , has its sides parallel to the corresponding sides of the original square, and each side of is tangent to one of the semicircles. The area of the square is
Problem 20
Let and be four different digits selected from the set
If the sum is to be as small as possible, then must equal
Problem 21
A gumball machine contains red, white, and blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is
Problem 22
The two wheels shown below are spun and the two resulting numbers are added. The probability that the sum is even is
Problem 23
If , and are different digits, then the largest possible digit sum for
has the form
Problem 24
A by square is divided into four by squares. Each of the small squares is to be painted either green or red. In how many different ways can the painting be accomplished so that no green square shares its top or right side with any red square? There may be as few as zero or as many as four small green squares.
Problem 25
Find the sum of the digits in the answer to
where a string of nines is multiplied by a string of fours.
See also
1994 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by 1993 AJHSME |
Followed by 1995 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.