Difference between revisions of "1986 AJHSME Problems"
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In the product shown, <math>\text{B}</math> is a digit. The value of <math>\text{B}</math> is | In the product shown, <math>\text{B}</math> is a digit. The value of <math>\text{B}</math> is | ||
− | <cmath>\begin{ | + | <cmath>\begin{array}{rr} |
− | \text{B}2 \\ | + | &\text{B}2 \\ |
− | \times 7\text{B} \\ \hline | + | \times &7\text{B} \\ \hline |
− | 6396 \\ | + | &6396 \\ |
− | \end{ | + | \end{array}</cmath> |
<math>\text{(A)}\ 3 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 8</math> | <math>\text{(A)}\ 3 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 8</math> |
Revision as of 19:34, 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
In July 1861, inches of rain fell in Cherrapunji, India. What was the average rainfall in inches per hour during that month?
Problem 2
Which of the following numbers has the largest reciprocal?
Problem 3
The smallest sum one could get by adding three different numbers from the set is
Problem 4
The product is closest to
Problem 5
A contest began at noon one day and ended minutes later. At what time did the contest end?
Problem 6
Problem 7
How many whole numbers are between and ?
Problem 8
In the product shown, is a digit. The value of is
Problem 9
Using only the paths and the directions shown, how many different routes are there from to ?
Problem 10
A picture feet across is hung in the center of a wall that is feet wide. How many feet from the end of the wall is the nearest edge of the picture?
Problem 11
If means , then is
Problem 12
The table below displays the grade distribution of the students in a mathematics class on the last two tests. For example, exactly one student received a 'D' on Test 1 and a 'C' on Test 2 (see circled entry). What percent of the students received the same grade on both tests?
Problem 13
The perimeter of the polygon shown is
Problem 14
If and , then the largest value of the quotient is
Problem 15
Sale prices at the Ajax Outlet Store are below original prices. On Saturdays an additional discount of off the sale price is given. What is the Saturday price of a coat whose original price is <dollar/>?
<dollar/>
<dollar/>
<dollar/>
<dollar/>
<dollar/>
Problem 16
A bar graph shows the number of hamburgers sold by a fast food chain each season. However, the bar indicating the number sold during the winter is covered by a smudge. If exactly of the chain's hamburgers are sold in the fall, how many million hamburgers are sold in the winter?
Problem 17
Let be an odd whole number and let be any whole number. Which of the following statements about the whole number is always true?
Problem 18
A rectangular grazing area is to be fenced off on three sides using part of a meter rock wall as the fourth side. Fence posts are to be placed every meters along the fence including the two posts where the fence meets the rock wall. What is the fewest number of posts required to fence an area m by m?
Problem 19
At the beginning of a trip, the mileage odometer read miles. The driver filled the gas tank with gallons of gasoline. During the trip, the driver filled his tank again with gallons of gasoline when the odometer read . At the end of the trip, the driver filled his tank again with gallons of gasoline. The odometer read . To the nearest tenth, what was the car's average miles-per-gallon for the entire trip?
Problem 20
The value of the expression is closest to
Problem 21
Suppose one of the eight lettered identical squares is included with the four squares in the T-shaped figure outlined. How many of the resulting figures can be folded into a topless cubical box?
Problem 22
Alan, Beth, Carlos, and Diana were discussing their possible grades in mathematics class this grading period. Alan said, "If I get an A, then Beth will get an A." Beth said, "If I get an A, then Carlos will get an A." Carlos said, "If I get an A, then Diana will get an A." All of these statements were true, but only two of the students received an A. Which two received A's?
Problem 23
The large circle has diameter . The two small circles have their centers on and just touch at , the center of the large circle. If each small circle has radius , what is the value of the ratio of the area of the shaded region to the area of one of the small circles?
Problem 24
The students at King Middle School are divided into three groups of equal size for lunch. Each group has lunch at a different time. A computer randomly assigns each student to one of three lunch groups. The probability that three friends, Al, Bob, and Carol, will be assigned to the same lunch group is approximately
Problem 25
Which of the following sets of whole numbers has the largest average?
See Also
1986 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by 1985 AJHSME |
Followed by 1987 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.