2024年AMC 10B 真题:
Problem 1
In a long line of people arranged left to right, the 1013th person from the left is also the 1010th person from the right. How many people are in the line?
Problem 2
What is
Problem 3
For how many integer values of is
?
Problem 4
Balls numbered are deposited in
bins, labeled
,
,
,
, and
using the following procedure. Ball
is deposited in bin
, and balls
and
are deposited in bin
. The next
balls are deposited in bin
, the next
in bin
, and so on, cycling back to bin
after balls are deposited in bin
. (For example, balls numbered
are deposited in bin
at step
of this process.) In which bin is ball
deposited?
Problem 5
In the following expression, Melanie changed some of the plus signs to minus signs:When the new expression was evaluated, it was negative. What is the least number of plus signs that Melanie could have changed to minus signs?
Problem 6
A rectangle has integer side lengths and an area of . What is the least possible perimeter of the rectangle?
Problem 7
What is the remainder when is divided by
?
Problem 8
Let be the product of all the positive integer divisors of
. What is the units digit of
?
Problem 9
Real numbers and
have arithmetic mean
. The arithmetic mean of
and
is
. What is the arithmetic mean of
and
?
Problem 10
Quadrilateral is a parallelogram, and
is the midpoint of the side
. Let
be the intersection of lines
and
. What is the ratio of the area of quadrilateral
to the area of
?
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