美国数学竞赛A试题.docx

美国数学竞赛A试题
 
 
What is the value of
?
Solution
For what value of
does
?
Solution
For every dollar Ben spent on bagels, David spent cents less. Ben paid
more than David. How much did they
spend in the bagel store together?
Solution
The remainder can be defined for all real numbers
and
with
by
where denotes the greatest integer less than or equal to . What is the value of ?
Solution
A rectangular box has integer side lengths in the ratio
. Which of the following could be the volume of the box?
Solution
Ximena lists the whole numbers through once. Emilio copies Ximena's numbers, replacing each occurrence of the digit by the digit . Ximena adds her numbers and Emilio adds his numbers. How much larger is Ximena's sum than Emilio's?
2016 AMC 10A Problems
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Solution
The mean, median, and mode of the data values
are all equal to
. What is the
value of ?
Solution
Trickster Rabbit agrees with Foolish Fox to double Fox's money every time Fox crosses the bridge by Rabbit's house, as long as Fox pays coins in toll to Rabbit after each crossing. The payment is made after the doubling, Fox is excited about his good fortune until he discovers that all his money is gone after crossing the bridge three times. How many coins did Fox have at the beginning?
Solution
A tri