Difference between revisions of "2008 AMC 12A Problems"
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([[2008 AMC 12A Problems/Problem 16|Solution]]) | ([[2008 AMC 12A Problems/Problem 16|Solution]]) | ||
==Problem 17== | ==Problem 17== | ||
| + | Let <math>a_1,a_2,\ldots</math> be a sequence determined by the rule <math>a_n=a_{n-1}/2</math> if <math>a_{n-1}</math> is even and <math>a_n=3a_{n-1}+1</math> if <math>a_{n-1}</math> is odd. For how many positive integers <math>a_1 \le 2008</math> is it true that <math>a_1</math> is less than each of <math>a_2</math>, <math>a_3</math>, and <math>a_4</math>? | ||
| + | |||
| + | <math>\textbf{(A)} 250 \qquad \textbf{(B)} 251 \qquad \textbf{(C)} 501 \qquad \textbf{(D)} 502 \qquad \textbf{(E)} 1004</math> | ||
([[2008 AMC 12A Problems/Problem 17|Solution]]) | ([[2008 AMC 12A Problems/Problem 17|Solution]]) | ||
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==Problem 18== | ==Problem 18== | ||
Revision as of 14:20, 17 February 2008
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
A bakery owner turns on his doughnut machine at 8:30 AM. At 11:10 AM the machine has completed one third of the day's job. At what time will the doughnut machine complete the job?
(Solution)
Problem 2
What is the reciprocal of 
?
(Solution)
Problem 3
(Solution)
Problem 4
(Solution)
Problem 5
(Solution)
Problem 6
Consider a function 
with domain ![$[0,2]$](http://latex.artofproblemsolving.com/9/0/7/9076ffb2b9c051f1b6f07bf18066581d57216258.png)
and range ![$[0,1]$](http://latex.artofproblemsolving.com/e/8/6/e861e10e1c19918756b9c8b7717684593c63aeb8.png)
. Let 
. What are the domain and range, respectively, of 
?
![$\textbf{(A)}\ [ - 1,1],[ - 1,0] \qquad \textbf{(B)}\ [ - 1,1],[0,1] \qquad \textbf{(C)}\ [0,2],[ - 1,0] \qquad \textbf{(D)}\ [1,3],[ - 1,0] \qquad \textbf{(E)}\ [1,3],[0,1]$](http://latex.artofproblemsolving.com/9/c/3/9c34c533e9603d76b4950aabba8383821c18cad2.png)
(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
Let 
be a sequence determined by the rule 
if 
is even and 
if is odd. For how many positive integers 
is it true that 
is less than each of 
, 
, and 
?
(Solution)
Problem 18
(Solution)
Problem 19
In the expansion of
,
what is the coefficient of 
?
(Solution)
Problem 20
(Solution)
Problem 21
(Solution)
Problem 22
(Solution)
Problem 23
(Solution)
Problem 24
(Solution)
Problem 25
(Solution)
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