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Difference between revisions of "2011 AMC 8 Problems"

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<math>\text{(A)} \text{median} < \text{mean} < \text{mode} \qquad \text{(B)} \text{mean} < \text{mode} < \text{median} \\ \\ \text{(C)} \text{mean} < \text{median} < \text{mode} \qquad \text{(D)} \text{median} < \text{mode} < \text{mean} \\ \\ \text{(E)} \text{mode} < \text{median} < \text{mean}</math>
 
<math>\text{(A)} \text{median} < \text{mean} < \text{mode} \qquad \text{(B)} \text{mean} < \text{mode} < \text{median} \\ \\ \text{(C)} \text{mean} < \text{median} < \text{mode} \qquad \text{(D)} \text{median} < \text{mode} < \text{mean} \\ \\ \text{(E)} \text{mode} < \text{median} < \text{mean}</math>
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==Solution==
 
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==See Also==
 
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{{AMC8 box|year=2011|num-b=3|num-a=5}}
 
  
 
[[2011 AMC 8 Problems/Problem 4|Solution]]
 
[[2011 AMC 8 Problems/Problem 4|Solution]]

Revision as of 17:04, 25 November 2011

Problem 1

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

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


Solution

Problem 2

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

$\text{(A) Karl's garden is larger by 100 square feet.}$

$\text{(B) Karl's garden is larger by 25 square feet.}$

$\text{(C) The gardens are the same size.}$

$\text{(D) Makenna's garden is larger by 25 square feet.}$

$\text{(E) Makenna's garden is larger by 100 square feet.}$


Solution

Problem 3

Solution

Problem 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?

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

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

A circle with radius $1$ is inscribed in a square and circumscribed about another square as shown. Which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?

[asy] filldraw((-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle,mediumgray,black); filldraw(Circle((0,0),1), mediumgray,black); filldraw((-1,0)--(0,1)--(1,0)--(0,-1)--cycle,white,black);[/asy]

$\text{(A)}\ \frac{1}2\qquad\text{(B)}\ 1\qquad\text{(C)}\ \frac{3}2\qquad\text{(D)}\ 2\qquad\text{(E)}\ \frac{5}2$


Solution

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