2008 AMC 12A Problems
Problem 1
A bakery owner turns on his doughnut machine at . At the machine has completed one third of the day's job. At what time will the doughnut machine complete the job?
Solution
The machine completes one-third of the job in hours. Thus, the entire job is completed in hours.
Since the machine was started at , the job will be finished hours later, at . The answer is .
Problem 2
What is the reciprocal of ?
Solution
.
Problem 3
Suppose that of bananas are worth as much as oranges. How many oranges are worth as much as of bananas?
Solution
If , then .
Problem 4
Which of the following is equal to the product
Solution
Solution 1
.
Solution 2
Notice that everything cancels out except for in the numerator and in the denominator.
Thus, the product is , and the answer is .
Problem 5
Suppose that is an integer. Which of the following statements must be true about ?
Solution
For to be an integer, must be even, but not necessarily divisible by . Thus, the answer is .
Problem 6
Heather compares the price of a new computer at two different stores. Store offers off the sticker price followed by a rebate, and store xposedoffers off the same sticker price with no rebate. Heather saves by buying the computer at store instead of store . What is the sticker price of the computer, in dollars?
Solution
Solution 1
Let the sticker price be .
The price of the computer is at store , and at store .
Heather saves at store , so .
Solving, we find , and the thus answer is .
Solution 2
The in store is better than the additional off at store .
Thus the off is equal to , and therefore the sticker price is .
Problem 7
While Steve and LeRoy are fishing 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 gallons per minute. The boat will sink if it takes in more than 30 gallons of water. Steve starts rowing toward the shore at a constant rate of 4 miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking?
Solution
It will take of an hour or minutes to get to shore.
Since only gallons of water can enter the boat, only net gallons can enter the boat per minute.
Since gallons of water enter the boat each minute, LeRoy must bail gallons per minute .
Problem 8
What is the volume of a cube whose surface area is twice that of a cube with volume 1?
Solution

版权声明：本站内容均来自互联网，仅供演示用，请勿用于商业和其他非法用途。如果侵犯了您的权益请与我们联系QQ:729038198，我们将在24小时内删除。