Difference between revisions of "2001 AMC 10 Problems"
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The state income tax where Kristin lives is levied at the rate of <math> p\% </math> of the first <math> \</math><math>28000 </math> of annual income plus <math> (p + 2)\% </math> of any amount above <math> \</math><math>28000 </math>. Kristin noticed that the state income tax she paid amounted to <math> (p + 0.25)\% </math> of her annual income. What was her annual income? | The state income tax where Kristin lives is levied at the rate of <math> p\% </math> of the first <math> \</math><math>28000 </math> of annual income plus <math> (p + 2)\% </math> of any amount above <math> \</math><math>28000 </math>. Kristin noticed that the state income tax she paid amounted to <math> (p + 0.25)\% </math> of her annual income. What was her annual income? | ||
| − | <math> \textbf{(A) }\< | + | <math> \textbf{(A) }\<cmath>28000\qquad\textbf{(B) }</cmath>32000\qquad\textbf{(C) }\<cmath>35000\qquad\textbf{(D) }</cmath>42,000\qquad\textbf{(E) }\</math><math>56000 </math> |
Revision as of 14:23, 16 March 2011
Contents
Problem 1
The median of the list 
is 
. What is the mean?
Problem 2
A number 
is 
more than the product of its reciprocal and its additive inverse. In which interval does the number lie?
Problem 3
The sum of two numbers is 
. Suppose 
is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?
Problem 4
What is the maximum number for the possible points of intersection of a circle and a triangle?
Problem 5
How many of the twelve pentominoes have at least one line of symmetry?
Problem 6
Let 
and 
denote the product and the sum, respectively, of the digits
of the integer 
. For example, 
and 
. Suppose 
is a
two-digit number such that 
. What is the units digit of ?
Problem 7
When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. What is the original number?
Problem 8
Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how many school days from today will they next be together tutoring in the lab?
Problem 9
The state income tax where Kristin lives is levied at the rate of 
of the first 
of annual income plus 
of any amount above . Kristin noticed that the state income tax she paid amounted to 
of her annual income. What was her annual income?
$\textbf{(A) }\<cmath>28000\qquad\textbf{(B) }</cmath>32000\qquad\textbf{(C) }\<cmath>35000\qquad\textbf{(D) }</cmath>42,000\qquad\textbf{(E) }$ (Error compiling LaTeX. Unknown error_msg)
