Algebra
Ryan got 80% of the problems correct on a 25-problem test, 90% on a 40-problem test, and 70% on a 10-problem test. What percent of all the problems did Ryan answer correctly?
84% (AMC 8 2010)
The area of a circle whose circumference is 24pi is k*pi. What is the value of k?
144 (AMC 10A 2010)
What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594?
330 (AMC 8 2013)
Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?
1/3 (AMC 8 2011)
What is the sum of the mean, median, and mode of the numbers 2, 3, 0, 3, 1, 4, 0, 3?
7.5 (AMC 8 2010)
David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15 miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles is the airport from his home?
210 (AMC 10A 2014)
Square EFGH has one vertex on each side of square ABCD. Point E is on AB with AE=7*EB. What is the ratio of the area of EFGH to the area of ABCD?
25/32 (AMC 10A 2011)
What is the units digit (ones place digit) of 13^2012?
1 (AMC 8 2012)
Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips?
5 (AMC 8 2011)
At the beginning of the school year, 50% of all students in Mr. Wells' math class answered "Yes" to the question "Do you love math", and 50% answered "No." At the end of the school year, 70% answered "Yes" and 30% answered "No." Altogether, x% of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of x?
60 (AMC 10B 2010)
Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?
5 (AMC 10A 2015)
Logan is constructing a scaled model of his town. The city's water tower stands 40 meters high, and the top portion is a sphere that holds 100,000 liters of water. Logan's miniature water tower holds 0.1 liters. How tall, in meters, should Logan make his tower?
0.4 (AMC 10A 2010)
Jamar bought some pencils costing more than a penny each at the school bookstore and paid $1.43. Sharona bought some of the same pencils and paid $1.87. How many more pencils did Sharona buy than Jamar?
4 (AMC 8 2012)
Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value?
7/72 (AMC 10B 2014)
Marvin had a birthday on Tuesday, May 27 in the leap year 2008. In what year will his birthday next fall on a Saturday?
2017 (AMC 10A 2010)
What is the sum of all the solutions of x=|2x-|60-2x||?
92 (2010 AMC 10B)
Circles A, B, and C each have radius 1. Circles A and B share one point of tangency. Circle C has a point of tangency with the midpoint of AB. What is the area inside circle C but outside circle A and circle B?
2 (AMC 10A 2011)
What is the smallest positive multiple of 45 that has only 0's and 1's as digits?
1,111,111,110 (AoPS Prealgebra textbook)
The number 2013 has the property that its units digit is the sum of its other digits, that is 2+0+1=3. How many integers less than 2013 but greater than 1000 share this property?
46 (AMC 10B 2013)
In the cryptarithm SEND + MORE = MONEY, what digit does the letter Y represent?
2 (AoPS Prealgebra textbook)