Found problems: 260
2016 AMC 8, 20
The least common multiple of $a$ and $b$ is $12$, and the least common multiple of $b$ and $c$ is $15$. What is the least possible value of the least common multiple of $a$ and $c$?
$\textbf{(A) }20\qquad\textbf{(B) }30\qquad\textbf{(C) }60\qquad\textbf{(D) }120\qquad \textbf{(E) }180$
2018 AMC 8, 1
An amusement park has a collection of scale models, with ratio $1 : 20$, of buildings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its replica to the nearest whole number?
$\textbf{(A) }14\qquad\textbf{(B) }15\qquad\textbf{(C) }16\qquad\textbf{(D) }18\qquad\textbf{(E) }20$
2018 AMC 8, 8
Mr. Garcia asked the members of his health class how many days last week they exercised for at least 30 minutes. The results are summarized in the following bar graph, where the heights of the bars represent the number of students.
[asy]
size(8cm);
void drawbar(real x, real h) {
fill((x-0.15,0.5)--(x+0.15,0.5)--(x+0.15,h)--(x-0.15,h)--cycle,gray);
}
draw((0.5,0.5)--(7.5,0.5)--(7.5,5)--(0.5,5)--cycle);
for (real i=1; i<5; i=i+0.5) {
draw((0.5,i)--(7.5,i),gray);
}
drawbar(1.0,1.0);
drawbar(2.0,2.0);
drawbar(3.0,1.5);
drawbar(4.0,3.5);
drawbar(5.0,4.5);
drawbar(6.0,2.0);
drawbar(7.0,1.5);
for (int i=1; i<8; ++i) {
label("$"+string(i)+"$",(i,0.25));
}
for (int i=1; i<9; ++i) {
label("$"+string(i)+"$",(0.5,0.5*(i+1)),W);
}
label("Number of Days of Exercise",(4,-0.1));
label(rotate(90)*"Number of Students",(-0.1,2.75));
[/asy]What was the mean number of days of exercise last week, rounded to the nearest hundredth, reported by the students in Mr. Garcia's class?
$\textbf{(A) } 3.50 \qquad \textbf{(B) } 3.57 \qquad \textbf{(C) } 4.36 \qquad \textbf{(D) } 4.50 \qquad \textbf{(E) } 5.00$
2020 AMC 8 -, 3
Carrie has a rectangular garden that measures $6$ feet by $8$ feet. She plants the entire garden with strawberry plants. Carrie is able to plant $4$ strawberry plants per square foot, and she harvests an average of $10$ strawberries per plant. How many strawberries can she expect to harvest?
$\textbf{(A)}\ 560 \qquad \textbf{(B)}\ 960 \qquad \textbf{(C)}\ 1120 \qquad \textbf{(D)}\ 1920 \qquad \textbf{(E)}\ 3840$
2023 AMC 8, 12
The figure below shows a large white circle with a number of smaller white and shaded circles in its interior. What fraction of the interior of the large white circle is shaded?
[asy]
size(5cm);
defaultpen(linewidth(1pt));
draw(circle((3,3),3));
filldraw(circle((5.5,3),0.5),mediumgray*0.5 + lightgray*0.5);
filldraw(circle((2,3),2),mediumgray*0.5 + lightgray*0.5);
filldraw(circle((1,3),1),white);
filldraw(circle((3,3),1),white);
add(grid(6,6,mediumgray*0.5+gray*0.5+linetype("4 4")));
filldraw(circle((4.5,4.5),0.5),mediumgray*0.5 + lightgray*0.5);
filldraw(circle((4.5,1.5),0.5),mediumgray*0.5 + lightgray*0.5);
[/asy]$\textbf{(A) } \dfrac14\qquad\textbf{(B) } \dfrac{11}{36}\qquad\textbf{(C) } \dfrac13\qquad\textbf{(D) } \dfrac{19}{36}\qquad\textbf{(E) } \dfrac59$
2023 AMC 8, 5
A lake contains $250$ trout, along with a variety of other fish. When a marine biologist catches and releases a sample of $180$ fish from the lake, $30$ are identified as trout. Assume that the ratio of trout to the total number of fish is the same in both the sample and the lake. How many fish are there in the lake?
$\textbf{(A)}~1250\qquad \textbf{(B)}~1500\qquad \textbf{(C)}~1750\qquad \textbf{(D)}~1800\qquad \textbf{(E)}~2000$
2010 Contests, 4
What is the sum of the mean, median, and mode of the numbers, $2,3,0,3,1,4,0,3$?
$ \textbf{(A)}\ 6.5 \qquad\textbf{(B)}\ 7\qquad\textbf{(C)}\ 7.5\qquad\textbf{(D)}\ 8.5\qquad\textbf{(E)}\ 9 $
2025 AMC 8, 20
Sarika, Dev, and Rajiv are sharing a large block of cheese. They take turns cutting off half of what remains and eating it: first Sarika eats half of the cheese, then Dev eats half of the remaining half, then Rajiv eats half of what remains, then back to Sarika, and so on. They stop when the cheese is too small to see. About what fraction of the original block of cheese does Sarika eat in total?
$\hspace*{5mm}\text{(A) } \frac{4}{7} \quad \text{(B) } \frac{3}{5} \quad \text{(C) } \frac{2}{3} \quad \text{(D) } \frac{3}{4} \quad \text{(E) } \frac{7}{8}$
2022 AMC 8 -, 15
Laszlo went online to shop for black pepper and found thirty different black pepper options varying in weight and price, shown in the scatter plot below. In ounces, what is the weight of the pepper that offers the lowest price per ounce?
[asy]
//diagram by pog
size(8.5cm);
usepackage("mathptmx");
defaultpen(mediumgray*0.5+gray*0.5+linewidth(0.63));
add(grid(6,6));
label(scale(0.7)*"$1$", (1,-0.3), black);
label(scale(0.7)*"$2$", (2,-0.3), black);
label(scale(0.7)*"$3$", (3,-0.3), black);
label(scale(0.7)*"$4$", (4,-0.3), black);
label(scale(0.7)*"$5$", (5,-0.3), black);
label(scale(0.7)*"$1$", (-0.3,1), black);
label(scale(0.7)*"$2$", (-0.3,2), black);
label(scale(0.7)*"$3$", (-0.3,3), black);
label(scale(0.7)*"$4$", (-0.3,4), black);
label(scale(0.7)*"$5$", (-0.3,5), black);
label(scale(0.75)*rotate(90)*"Price (dollars)", (-1,3.2), black);
label(scale(0.75)*"Weight (ounces)", (3.2,-1), black);
dot((1,1.2),black);
dot((1,1.7),black);
dot((1,2),black);
dot((1,2.8),black);
dot((1.5,2.1),black);
dot((1.5,3),black);
dot((1.5,3.3),black);
dot((1.5,3.75),black);
dot((2,2),black);
dot((2,2.9),black);
dot((2,3),black);
dot((2,4),black);
dot((2,4.35),black);
dot((2,4.8),black);
dot((2.5,2.7),black);
dot((2.5,3.7),black);
dot((2.5,4.2),black);
dot((2.5,4.4),black);
dot((3,2.5),black);
dot((3,3.4),black);
dot((3,4.2),black);
dot((3.5,3.8),black);
dot((3.5,4.5),black);
dot((3.5,4.8),black);
dot((4,3.9),black);
dot((4,5.1),black);
dot((4.5,4.75),black);
dot((4.5,5),black);
dot((5,4.5),black);
dot((5,5),black);
[/asy]
$\textbf{(A)} ~1\qquad\textbf{(B)} ~2\qquad\textbf{(C)} ~3\qquad\textbf{(D)} ~4\qquad\textbf{(E)} ~5\qquad$
2024 AMC 8 -, 12
Rohan keeps a total of 90 guppies in 4 fish tanks.
There is 1 more guppy in the 2nd tank than the 1st tank.
There are 2 more guppies the the 3rd tank than the 2nd tank.
There are 3 more guppies in the 4th tank than the 3rd tank.
How many guppies are in the 4th tank?
$\textbf{(A) } 20\qquad\textbf{(B) } 21\qquad\textbf{(C) } 23\qquad\textbf{(D) } 24\qquad\textbf{(E) } 26$