Difference between revisions of "2013 AMC 8 Problems"
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| − | <math> \textbf{(A)}\ | + | If <math>3^p + 3^4 = 90</math>, <math>2^r + 44 = 76</math>, and <math>5^3 + 6^s = 1421</math>, what is the product of <math>p</math>, <math>r</math>, and <math>s</math>? |
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| + | <math> \textbf{(A)}\ 27\qquad\textbf{(B)}\ 40\qquad\textbf{(C)}\ 50\qquad\textbf{(D)}\ 70\qquad\textbf{(E)}\ 90 </math> | ||
[[2013 AMC 8 Problems/Problem 15|Solution]] | [[2013 AMC 8 Problems/Problem 15|Solution]] | ||
Revision as of 12:33, 27 November 2013
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
Problem 1
Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way?
Problem 2
A sign at the fish market says, "50% off, today only: half-pound packages for just $3 per package." What is the regular price for a full pound of fish, in dollars?
Problem 3
What is the value of 
?
Problem 4
Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill?
$\textbf{(A)}\ $120\qquad\textbf{(B)}\ $128\qquad\textbf{(C)}\ $140\qquad\textbf{(D)}\ $144\qquad\textbf{(E)}\ $160$ (Error compiling LaTeX. Unknown error_msg)
Problem 5
Hammie is in the 
grade and weighs 106 pounds. His quadruplet sisters are tiny babies and weigh 5, 5, 6, and 8 pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds?
Problem 6
The number in each box below is the product of the numbers in the two boxes that touch it in the row above. For example, 
. What is the missing number in the top row?
![[asy] unitsize(0.8cm); draw((-1,0)--(1,0)--(1,-2)--(-1,-2)--cycle); draw((-2,0)--(0,0)--(0,2)--(-2,2)--cycle); draw((0,0)--(2,0)--(2,2)--(0,2)--cycle); draw((-3,2)--(-1,2)--(-1,4)--(-3,4)--cycle); draw((-1,2)--(1,2)--(1,4)--(-1,4)--cycle); draw((1,2)--(1,4)--(3,4)--(3,2)--cycle); label("600",(0,-1)); label("30",(-1,1)); label("6",(-2,3)); label("5",(0,3)); [/asy]](http://latex.artofproblemsolving.com/6/f/f/6ff959a8ad5edfb7806895cbf5fa087e79899f3f.png)
Problem 7
Trey and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted 6 cars in the first 10 seconds. It took the train 2 minutes and 45 seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train?
Problem 8
A fair coin is tossed 3 times. What is the probability of at least two consecutive heads?
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. By which of the following might her incorrect sum have differed from the correct one?
Problem 14
Abe holds 1 green and 1 red jelly bean in his hand. Bea holds 1 green, 1 yellow, and 2 red jelly beans in her hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match?
Problem 15
If 
, 
, and 
, what is the product of 
, 
, and 
?
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks wide. How many toothpicks are used altogether?
[asy] picture corner; draw(corner,(5,0)--(35,0)); draw(corner,(0,-5)--(0,-35)); for (int i=0; i<3; ++i) { for (int j=0; j>-2; --j) { if ((i-j)<3) { add(corner,(50i,50j)); } } } draw((5,-100)--(45,-100)); draw((155,0)--(185,0),dotted); draw((105,-50)--(135,-50),dotted); draw((100,-55)--(100,-85),dotted); draw((55,-100)--(85,-100),dotted); draw((50,-105)--(50,-135),dotted); draw((0,-105)--(0,-135),dotted); [/asy]
Problem 23
Problem 24
Problem 25
Solution
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
