Difference between revisions of "2024 AMC 8 Problems"
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==Problem 16== | ==Problem 16== | ||
Minh enters the numbers <math>1</math> through <math>81</math> into the cells of a <math>9 \times 9</math> grid in some order. She calculates the product of the numbers in each row and column. What is the least number of rows and columns that could have a product divisible by <math>3</math>? | Minh enters the numbers <math>1</math> through <math>81</math> into the cells of a <math>9 \times 9</math> grid in some order. She calculates the product of the numbers in each row and column. What is the least number of rows and columns that could have a product divisible by <math>3</math>? | ||
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+ | <math>\textbf{(A) } 8\qquad\textbf{(B) } 9\qquad\textbf{(C) } 10\qquad\textbf{(D) } 11\qquad\textbf{(E) } 12</math> | ||
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+ | [[2024 AMC 8 Problems/Problem 16|Solution]] | ||
==Problem 17== | ==Problem 17== |
Revision as of 17:19, 25 January 2024
2024 AMC 8 (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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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 |
Contents
- 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 10
- 10 Problem 11
- 11 Problem 12
- 12 Problem 13
- 13 Problem 14
- 14 Problem 15
- 15 Problem 16
- 16 Problem 17
- 17 Problem 18
- 18 Problem 19
- 19 Problem 20
- 20 Problem 21
- 21 Problem 22
- 22 Problem 23
- 23 Problem 24
- 24 Problem 25
- 25 See Also
Problem 1
What is the ones digit of
Problem 2
What is the value of this expression in decimal form?
Problem 3
Four squares of side lengths , , , and units are arranged in increasing size order so that their left edges and bottom edges align. The squares alternate in the color pattern white-gray-white-gray, respectively, as shown in the figure. What is the area of the visible gray region in square units?
[DIAGRAM]
Problem 4
When Yunji added all the integers from to , she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out?
Problem 5
Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of . Which of the following integers cannot be the sum of the two numbers?
Problem 6
Sergai skated around an ice rink, gliding along different paths. The gray lines in the figures below show foru of the paths labeled , , , and . What is the sorted order of the four paths from shortest to longest?
[DIAGRAM]
Problem 7
A x rectangle is covered without overlap by 3 shapes of tiles: x, x, and x, shown below. What is the minimum possible number of x tiles used?
(A) (B) (C) (D) (E)
Problem 8
On Monday Taye has $2. Every day, he either gains $3 or doubles the amount of money he had on the previous day. How many different dollar amounts could Taye have on Thursday, 3 days later?
Problem 10
In January 1980 the Mauna Loa Observatory recorded carbon dioxide (CO_2) levels of 338 ppm (parts per million). Over the years the average CO_2 reading has increased by about 1.1516 ppm each year. What is the expected CO_2 level in ppm in January 2030? Round your answer to the nearest integer.
Problem 11
Problem 12
Problem 13
Buzz Bunny is hopping up and down a set of stairs, one step at a time. In how many ways can Buzz start on the ground, make a sequence of hops, and end up back on the ground? (For example, one sequence of hops is up-up-down-down-up-down.)
Problem 14
Problem 15
Let the letters ,,,,, represent distinct digits. Suppose is the greatest number that satisfies the equation
What is the value of ?
Problem 16
Minh enters the numbers through into the cells of a grid in some order. She calculates the product of the numbers in each row and column. What is the least number of rows and columns that could have a product divisible by ?
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
A group of frogs (called an army) is living in a tree. A frog turns green when in the shade and turns yellow when in the sun. Initially, the ratio of green to yellow frogs was . Then green frogs moved to the sunny side and yellow frogs moved to the shady side. Now the ratio is . What is the difference between the number of green frogs and the number of yellow frogs now?
Problem 22
Problem 23
Rodrigo is drawing lines on the coordinate plane, and counting how many unit squares they go through. He draws a line with endpoints and How many unit squares does this segment go through?
Problem 24
Jean has made a piece of stained glass art in the shape of two mountains, as shown in the figure below. One mountain peak is feet high while the other peak is feet high. Each peak forms a angle, and the straight sides form a angle with the ground. The artwork has an area of square feet. The sides of the mountain meet at an intersection point near the center of the artwork, feet above the ground. What is the value of
Problem 25
A small airplane has rows of seats with seats in each row. Eight passengers have boarded the plane and are distributed randomly among the seats. A married couple is next to board. What is the probability there will be adjacent seats in the same row for the couple?
[DIAGRAM]
See Also
2024 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by 2023 AMC 8 |
Followed by 2025 AMC 8 | |
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 AJHSME/AMC 8 Problems and Solutions |