2010 AMC 12B Problems
Contents
Problem 1
Makarla attended two meetings during her -hour work day. The first meeting took minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings?
Problem 2
A big is formed as shown. What is its area?
Problem 3
A ticket to a school play cost dollars, where is a whole number. A group of 9th graders buys tickets costing a total of $, and a group of 10th graders buys tickets costing a total of $. How many values for are possible?
Problem 4
A month with days has the same number of Mondays and Wednesdays.How many of the seven days of the week could be the first day of this month?
Problem 5
Lucky Larry's teacher asked him to substitute numbers for , , , , and in the expression and evaluate the result. Larry ignored the parenthese but added and subtracted correctly and obtained the correct result by coincidence. The number Larry sustitued for , , , and were , , , and , respectively. What number did Larry substitude for ?
Problem 6
At the beginning of the school year, of all students in Mr. Wells' math class answered "Yes" to the question "Do you love math", and answered "No." At the end of the school year, answered "Yes" and answerws "No." Altogether, 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 ?
Problem 7
Shelby drives her scooter at a speed of miles per hour if it is not raining, and miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the evening, for a total of miles in minutes. How many minutes did she drive in the rain?
Problem 8
Every high school in the city of Euclid sent a team of students to a math contest. Each participant in the contest received a different score. Andrea's score was the median among all students, and hers was the highest score on her team. Andrea's teammates Beth and Carla placed th and th, respectively. How many schools are in the city?
Problem 9
Let be the smallest positive integer such that id divisible by , is a perfect cube, and is a perfect square. What is the number of digits of ?
Problem 10
The average of the numbers and is . What is ?
Problem 11
A palindrome between and is chosen at random. What is the probability that it is divisible by ?
Problem 12
For what value of does
Problem 13
In , and . What is ?
Problem 14
Let , , , , and be postive integers with and let be the largest of the sum , , and . What is the smallest possible value of ?
Problem 15
For how many ordered triples of nonnegative integers less than are there exactly two distinct elements in the set , where ?
Problem 16
Positive integers , , and are randomly and independently selected with replacement from the set . What is the probability that is divisible by ?
Problem 17
The entries in a array include all the digits from through , arranged so that the entries in every row and column are in increasing order. How many such arrays are there?
Solution More coming -- 1:26 EDT 4/2/10