2011 AMC 8

$1.$ Margie bought $3$ apples at a cost of $50$ cents each. She paid with a $5$ -dollar bill. How much change did Margie receive?

$\textbf{(A)}1.50\qquad\textbf{(B)}2.00\qquad\textbf{(C)}2.50\qquad\textbf{(D)}3.00\qquad\textbf{(E)}3.50$

$2.$ Karl's rectangular vegetable garden is $20$ by $45$ feet, and Makenna's is $25$ by $40$ feet. Which garden is larger in area?

$\textbf{(A)}$ Karl's garden is larger by 100 square feet. $\textbf{(B)}$ Karl's garden is larger by 25 square feet. $\textbf{(C)}$ The gardens are the same size. $\textbf{(D)}$ Makenna's garden is larger by 25 square feet. $\textbf{(E)}$ Makenna's garden is larger by 100 square feet.

$3.$

$4.$ Here is a list of the numbers of fish that Tyler caught in nine outings last summer: $2,0,1,3,0,3,3,1,2.$ Which statement about the mean, median, and mode is true?

$\textbf{(A)} \text{median} < \text{mean} < \text{mode} \qquad \textbf{(B)} \text{mean} < \text{mode} < \text{median} \\ \\ \textbf{(C)} \text{mean} < \text{median} < \text{mode} \qquad \textbf{(D)} \text{median} < \text{mode} < \text{mean} \\ \\ \textbf{(E)} \text{mode} < \text{median} < \text{mean}$

$5.$ What time was it $2011$ minutes after midnight on January 1, 2011?

$\textbf{(A)} \text{January 1 at 9:31PM}$ $\textbf{(B)} \text{January 1 at 11:51PM}$ $\textbf{(C)} \text{January 2 at 3:11AM}$ $\textbf{(D)} \text{January 2 at 9:31AM}$ $\textbf{(E)} \text{January 2 at 6:01PM}$

$6.$ In a town of 351 adults, every adult owns a car, motorcycle, or both. If 331 adults own cars and 45 adults own motorcycles, how many of the car owners do not own a motorcycle?

$\textbf{(A)} 20 \qquad\textbf{(B)} 25 \qquad\textbf{(C)} 45 \qquad\textbf{(D)} 306 \qquad\textbf{(E)} 351$

$7.$

$8.$ Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips?

$\textbf{(A)} 4 \qquad\textbf{(B)} 5 \qquad\textbf{(C)} 6 \qquad\textbf{(D)} 7 \qquad\textbf{(E)} 9$

$9.$

$10.$ The taxi fare in Gotham City is $$$ 2.40 for the first $\frac12$ mile and additional mileage charged at the rate $$$ 0.20 for each additional 0.1 mile. You plan to give the driver a $$$ 2 tip. How many miles can you ride for $$$ 10?

$11.$

$12.$ Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?

$\textbf{(A)} \frac14 \qquad\textbf{(B)} \frac13 \qquad\textbf{(C)} \frac12 \qquad\textbf{(D)} \frac23 \qquad\textbf{(E)} \frac34$

$13.$

$14.$ There are $270$ students at Colfax Middle School, where the ratio of boys to girls is $5 : 4$ . There are $180$ students at Winthrop Middle School, where the ratio of boys to girls is $4 : 5$ . The two schools hold a dance and all students from both schools attend. What fraction of the students at the dance are girls?

$\textbf{(A)} \dfrac7{18} \qquad\textbf{(B)} \dfrac7{15} \qquad\textbf{(C)} \dfrac{22}{45} \qquad\textbf{(D)} \dfrac12 \qquad\textbf{(E)} \dfrac{23}{45}$

$15.$ How many digits are in the product $4^5 \cdot 5^{10}$ ?

$\textbf{(A)}8\qquad\textbf{(B)}9\qquad\textbf{(C)}10\qquad\textbf{(D)}11\qquad\textbf{(E)}15$

$16.$ Let $A$ be the area of a triangle with sides of length $25$ , $25$ , and $30$ . Let $B$ be the area of a triangle with sides of length $25$ , $25$ , and $40$ . What is the relationship between $A$ and $B$ ?

$\textbf{(A)}A = \dfrac9{16} B\qquad\textbf{(B)}A = \dfrac3{4} B\qquad\textbf{(C)}A = B\qquad\textbf{(D)}A = \dfrac4{3} B\qquad\textbf{(E)}A = \dfrac{16}{9} B$

$17.$ Let $w$ , $x$ , $y$ , and $z$ be whole numbers. If $2^w \cdot 3^x \cdot 5^y \cdot 7^z = 588$ , then what does $2w + 3x + 5y + 7z$ equal?

$\textbf{(A)}21\qquad\textbf{(B)}25\qquad\textbf{(C)}27\qquad\textbf{(D)}35\qquad\textbf{(E)}56$

$18.$ A fair six-sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number?

$\textbf{(A)}\dfrac1{6}\qquad\textbf{(B)}\dfrac5{12}\qquad\textbf{(C)}\dfrac1{2}\qquad\textbf{(D)}\dfrac7{12}\qquad\textbf{(E)}\dfrac5{6}$

$19.$ How many rectangles are in this figure?

$[asy] pair A,B,C,D,E,F,G,H,I,J,K,L; A=(0,0); B=(20,0); C=(20,20); D=(0,20); draw(A--B--C--D--cycle); E=(-10,-5); F=(13,-5); G=(13,5); H=(-10,5); draw(E--F--G--H--cycle); I=(10,-20); J=(18,-20); K=(18,13); L=(10,13); draw(I--J--K--L--cycle);[/asy]$ (Error compiling LaTeX. Unknown error_msg)

$\textbf{(A)}\ 8\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 11\qquad\textbf{(E)}\ 12$

$20.$

$21.$ Students guess that Norb's age is $24$ , $28$ , $30$ , $32$ , $36$ , $38$ , $41$ , $44$ , $47$ , and $49$ . Norb says, "At least half of you guessed too low, two of you are off by one and my age is a prime number." How old is he?

$\textbf{(A)}29\qquad\textbf{(B)}31\qquad\textbf{(C)}37\qquad\textbf{(D)}43\qquad\textbf{(E)}48$

$22.$ What is the tens digit of $7^{2011}$ ?

$\textbf{(A)}0\qquad\textbf{(B)}1\qquad\textbf{(C)}3\qquad\textbf{(D)}4\qquad\textbf{(E)}7$

$23.$ How many 4-digit positive integers have four different digits, where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit?

$\textbf{(A)}24\qquad\textbf{(B)}48\qquad\textbf{(C)}60\qquad\textbf{(D)}84\qquad\textbf{(E)}108$

$24.$ In how many ways can $10,001$ be written as the sum of two primes?

$\textbf{(A)}0\qquad\textbf{(B)}1\qquad\textbf{(C)}2\qquad\textbf{(D)}3\qquad\textbf{(E)}4$

$25.$

Page

Toolbox

Search

2011 AMC 8