AMC8
Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way?
1
The area of a rectangle is 24 in2 . If the length of the rectangle is 1.5 times its width, what is the rectangle’s perimeter?
20
Arvin ate 11 halves of tarts, Bernice ate 12 quarters of tarts, Chrisandra ate 13 eighths of tarts, and Drake ate 14 sixteenths of tarts. How many tarts were eaten?
11
Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill?
140
A positive integer less than 100 has fewer than six positive factors. What is the greatest possible value of this integer?
97
Janet played a song on her clarinet in 3 minutes and 20 seconds. Janet’s goal is to play the song at a 25% faster rate. Find the number of seconds it will take Janet to play the song when she reaches her goal.
160
A fair coin is tossed 3 times. What is the probability of at least two consecutive heads?
3/8
Stephanie rolls three standard dice. What is the probability that the product of the three numbers she rolled is not a multiple of 8? Express your answer as a common fraction.
2/3
Find the least positive integer whose digits add to a multiple of 27 yet the number itself is not a multiple of 27. For example, 87999921 is one such number.
1899
Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many gold coins did I have?
45
What is the least nine-digit positive integer that contains each of the digits from 1 to 9 exactly once, and is divisible by 99?
123,475,869
How many non-congruent isosceles triangles (including equilateral triangles) have positive integer side lengths and perimeter less than 20?
41
Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by 5 minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?
25
Edward has a meeting at 4:00 p.m. He leaves his house at a random time between 3:00 p.m. and 3:30 p.m., and due to traffic, it takes him a random length of time between 30 and 45 minutes to get to the meeting from his house. What is the probability that Edward arrives early? Express your answer as a common fraction.
3/4
The Purple Plant Garden Store sells grass seed in ten-pound bags and fifteen-pound bags. Yesterday half of the grass seed they had was in ten-pound bags. This morning the store received a shipment of 27 more ten-pound bags, and now they have twice as many ten-pound bags as fifteen-pound bags. Find the total weight in pounds of grass seed the store now has.
1890