1995 AJHSME Problems
1995 AJHSME (Answer Key) Printable version: | AoPS Resources • PDF | ||
Instructions
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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
Walter has exactly one penny, one nickel, one dime and one quarter in his pocket. What percent of one dollar is in his pocket?
Problem 2
Jose is years younger than Zack. Zack is years older than Inez. Inez is years old. How old is Jose?
Problem 3
Which of the following operations has the same effect on a number as multiplying by and then dividing by ?
Problem 4
A teacher tells the class,
"Think of a number, add 1 to it, and double the result. Give the answer to your partner. Partner, subtract 1 from the number you are given and double the result to get your answer."
Ben thinks of , and gives his answer to Sue. What should Sue's answer be?
Problem 5
Find the smallest whole number that is larger than the sum
Problem 6
Figures , , and are squares. The perimeter of is and the perimeter of is . The perimeter of is
Problem 7
At Clover View Junior High, one half of the students go home on the school bus. One fourth go home by automobile. One tenth go home on their bicycles. The rest walk home. What fractional part of the students walk home?
Problem 8
An American traveling in Italy wishes to exchange American money (dollars) for Italian money (lire). If 3000 lire = $1.60, how much lire will the traveler receive in exchange for $1.00?
Problem 9
Three congruent circles with centers , , and are tangent to the sides of rectangle as shown. The circle centered at has diameter and passes through points and . The area of the rectangle is
Problem 10
A jacket and a shirt originally sold for 80 dollars and 40 dollars, respectively. During a sale Chris bought the 80 dollar jacket at a discount and the 40 dollar shirt at a discount. The total amount saved was what percent of the total of the original prices?
.
Problem 11
Jane can walk any distance in half the time it takes Hector to walk the same distance. They set off in opposite directions around the outside of the 18-block area as shown. When they meet for the first time, they will be closest to
Problem 12
A lucky year is one in which at least one date, when written in the form month/day/year, has the following property: The product of the month times the day equals the last two digits of the year. For example, 1956 is a lucky year because it has the date 7/8/56 and . Which of the following is NOT a lucky year?
Problem 13
In the figure, , , and are right angles. If and , then
Problem 14
A team won 40 of its first 50 games. How many of the remaining 40 games must this team win so it will have won exactly 70% of its games for the season?
Problem 15
What is the digit to the right of the decimal point in the decimal form of ?
Problem 16
Students from three middle schools worked on a summer project.
- Seven students from Allen school worked for 3 days.
- Four students from Balboa school worked for 5 days.
- Five students from Carver school worked for 9 days.
The total amount paid for the students' work was . Assuming each student received the same amount for a day's work, how much did the students from Balboa school earn altogether?
Problem 17
The table below gives the percent of students in each grade at Annville and Cleona elementary schools:
Annville has 100 students and Cleona has 200 students. In the two schools combined, what percent of the students are in grade 6?
Problem 18
The area of each of the four congruent L-shaped regions of this 100-inch by 100-inch square is 3/16 of the total area. How many inches long is the side of the center square?
Problem 19
The graph shows the distribution of the number of children in the families of the students in Ms. Jordan's English class. The median number of children in the family for this distribution is
Problem 20
Diana and Apollo each roll a standard die obtaining a number at random from 1 to 6. What is the probability that Diana's number is larger than Apollo's number?
Problem 21
A plastic snap-together cube has a protruding snap on one side and receptacle holes on the other five sides as shown. What is the smallest number of these cubes that can be snapped together so that only receptacle holes are showing?
Problem 22
The number 6545 can be written as a product of a pair of positive two-digit numbers. What is the sum of this pair of numbers?
Problem 23
How many four-digit whole numbers are there such that the leftmost digit is odd, the second digit is even, and all four digits are different?
Problem 24
In parallelogram , is the altitude to the base and is the altitude to the base . [Note: Both pictures represent the same parallelogram.] If , , and , then
Problem 25
Buses from Dallas to Houston leave every hour on the hour. Buses from Houston to Dallas leave every hour on the half hour. The trip from one city to the other takes 5 hours. Assuming the buses travel on the same highway, how many Dallas-bound buses does a Houston-bound bus pass in the highway (not in the station)?
See also
1995 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by 1994 AJHSME |
Followed by 1996 AJHSME | |
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All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.