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Difference between revisions of "2005 AMC 12B Problems"

(→‎Problem 3)
(→‎Problem 4)
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== Problem 4 ==
 
== Problem 4 ==
−
The average (mean) of <math>20</math> numbers is <math>30, and the average of </math>30<math> other numbers is </math>20<math>.  What is the average of
+
At the beginning of the school year, Lisa's goal was to earn an A on at least <math>80\%</math> of her <math>50</math> quizzes for the year.  She earned an A on <math>22</math> of the first <math>30</math> quizzes.  If she is to achieve her goal, on at most how many of the remaining quizzes can she earn a grade lower than an A?
  
 +
<math>
 +
\mathrm{(A)}\ 1      \qquad
 +
\mathrm{(B)}\ 2      \qquad
 +
\mathrm{(C)}\ 3      \qquad
 +
\mathrm{(D)}\ 4      \qquad
 +
\mathrm{(E)}\ 5
 
</math>
 
</math>
−
\mathrm{(A)}\ \frac14x^2      \qquad
 
−
\mathrm{(B)}\ \frac25x^2      \qquad
 
−
\mathrm{(C)}\ \frac12x^2      \qquad
 
−
\mathrm{(D)}\ x^2      \qquad
 
−
\mathrm{(E)}\ \frac32x^2
 
−
$
 
  
 
[[2005 AMC 12B Problems/Problem 4|Solution]]
 
[[2005 AMC 12B Problems/Problem 4|Solution]]

Revision as of 21:15, 17 April 2009

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Problem 1

A scout troop buys $1000$ candy bars at a price of five for $2$ dollars. They sell all the candy bars at the price of two for $1$ dollar. What was their profit, in dollars?

$\mathrm{(A)}\ 100 \qquad \mathrm{(B)}\ 200 \qquad \mathrm{(C)}\ 300 \qquad \mathrm{(D)}\ 400 \qquad \mathrm{(E)}\ 500$

Solution

Problem 2

A positive number $x$ has the property that $x\%$ of $x$ is $4$. What is $x$? $\mathrm{(A)}\ 2 \qquad \mathrm{(B)}\ 4 \qquad \mathrm{(C)}\ 10 \qquad \mathrm{(D)}\ 20 \qquad \mathrm{(E)}\ 40$

Solution

Problem 3

Brianna is using part of the money she earned on her weekend job to buy several equally-priced CDs. She used one fifth of her money to buy one third of the CDs. What fraction of her money will she have left after she buys all the CDs?

$\mathrm{(A)}\ \frac15 \qquad \mathrm{(B)}\ \frac13 \qquad \mathrm{(C)}\ \frac25 \qquad \mathrm{(D)}\ \frac23 \qquad \mathrm{(E)}\ \frac45$

Solution

Problem 4

At the beginning of the school year, Lisa's goal was to earn an A on at least $80\%$ of her $50$ quizzes for the year. She earned an A on $22$ of the first $30$ quizzes. If she is to achieve her goal, on at most how many of the remaining quizzes can she earn a grade lower than an A?

$\mathrm{(A)}\ 1 \qquad \mathrm{(B)}\ 2 \qquad \mathrm{(C)}\ 3 \qquad \mathrm{(D)}\ 4 \qquad \mathrm{(E)}\ 5$

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

Solution

See also

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