2024 AMC 8 Solutions

What is the ones digit of 222,222 - 22,222 - 2,222 - 222 - 22 - 2?

• 0

• 2

• 4

• 6

• 8

Answer explanation

To find the ones digit of 222,222 - 22,222 - 2,222 - 222 - 22 - 2, we can focus on the ones digits of each number: 2 - 2 - 2 - 2 - 2 - 2 = 2. Thus, the ones digit of the result is 2.

Tags

CCSS.3.OA.D.9

What is the value of this expression in decimal form? 44/11 + 110/44 + 44/1100

• 6.4

• 6.504

• 6.54

• 6.9

• 6.94

Answer explanation

To solve the expression, calculate each term: 44/11 = 4, 110/44 = 2.5, and 44/1100 = 0.04. Adding these gives 4 + 2.5 + 0.04 = 6.54. Thus, the correct answer is 6.54.

Tags

CCSS.5.NBT.B.7

Four squares of side length 4, 7, 9, and 10 units are arranged in increasing size order so that their left edges and bottom edges align. The squares alternate in color white-gray-white-gray, respectively, as shown in the figure. What is the area of the visible gray region in square units?

• 42

• 45

• 49

• 50

• 52

Answer explanation

The area of the gray squares (7x7 and 10x10) is 49 + 100 = 149. The total area of all squares is 16 + 49 + 81 + 100 = 246. The visible gray area is 149 - (246 - 149) = 52 square units.

When Yunji added all the integers from 1 through 9, she mistakenly left out a number. Her incorrect sum turned out to be a square number. Which number did Yunji leave out?

• 5

• 6

• 7

• 8

• 9

Answer explanation

The sum of integers from 1 to 9 is 45. If Yunji left out 9, the sum becomes 36, which is a perfect square (6^2). Leaving out any other number does not yield a square. Thus, she left out 9.

Tags

CCSS.7.EE.B.3

Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of 6. Which of the following integers cannot be the sum of the two numbers?

• 5

• 6

• 7

• 8

• 9

Answer explanation

The product of two numbers is a multiple of 6 if at least one number is even and at least one is a multiple of 3. The sum of 5 (1+4 or 2+3) cannot yield a product that meets these criteria, making it impossible.

Sergei skated around an ice rink, gliding along different paths. The gray lines in the figures below show four of the paths labeled P, Q, R, and S. What is the sorted order of the four paths from shortest to longest?

• P, Q, R, S

• P, R, S, Q

• Q, S, P, R

• R, P, S, Q

• R, S, P, Q

Answer explanation

To determine the lengths of paths P, Q, R, and S, we analyze their shapes. Path R is the shortest, followed by P, then S, and finally Q, making the sorted order R, P, S, Q.

Tags

CCSS.2.MD.A.3

A 3 × 7 rectangle is covered without overlap by 3 shapes of tiles: 2 × 2, 1 × 4, and 1 × 1. What is the minimum possible number of 1 × 1 tiles used?

• 1

• 2

• 3

• 4

• 5

Answer explanation

To cover a 3 × 7 rectangle, we can use one 2 × 2 tile (covering 4 squares) and one 1 × 4 tile (covering 4 squares), leaving 3 squares uncovered. Thus, we need at least 5 of the 1 × 1 tiles to fill the remaining space.

Tags

CCSS.3.MD.C.5A

• 3

• 4

• 5

• 6

• 7

Answer explanation

Starting with $2, Taye can either gain $3 or double his amount each day. By Thursday, he can have $2, $5, $6, $8, $10, or $12, resulting in 6 different amounts.

All of the marbles in Maria’s collection are red, green, or blue. Maria has half as many red marbles as green marbles and twice as many blue marbles as green marbles. Which of the following could be the total number of marbles in Maria’s collection?

• 24

• 25

• 26

• 27

• 28

Answer explanation

Let green marbles be g. Then red marbles = g/2 and blue marbles = 2g. Total = g + g/2 + 2g = 4.5g. For total to be an integer, g must be even. If g = 8, total = 36; if g = 4, total = 18; if g = 6, total = 27; if g = 8, total = 28.

Tags

CCSS.7.EE.B.3

In January 1980 the Mauna Loa Observatory recorded carbon dioxide (CO₂) levels of 338 ppm. Over the years the average CO₂ reading has increased by about 1.515 ppm each year. What is the expected CO₂ level in ppm in January 2030? Round your answer to the nearest integer.

• 399

• 414

• 420

• 444

• 459

Answer explanation

From January 1980 to January 2030 is 50 years. The increase in CO₂ levels is 1.515 ppm/year, so 50 * 1.515 = 75.75 ppm. Adding this to the 1980 level: 338 + 75.75 = 413.75, rounded to 414 ppm.

Tags

CCSS.HSF.BF.A.2