2024 AMC 10B Problems
2024 AMC 10B (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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Problems to be added after the competition.
Contents
[hide]- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
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 line?
Problem 2
What is
Problem 3
For how many integer values of is
Problem 4
Balls numbered 1, 2, 3, ... are deposited in 5 bins, labeled A, B, C, D, and E, using the following procedure. Ball 1 is deposited in bin A, and balls 2 and 3 are deposited in bin B. The next 3 balls are deposited in bin C, the next 4 in bin D, and so on, cycling back to bin A after balls are deposited in bin E. (For example, balls numbered 22, 23, ..., 28 are deposited in bin B at step 7 of this process.) In which bin is ball 2024 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 length sides and an area of 2024. 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 posidive integer divisors of . What is the units digit of ?
Problem 9
Problem 10
Quasidrilateral 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 triangle ?
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
See also
2024 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by 2024 AMC 10A Problems |
Followed by 2025 AMC 10A Problems | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.