# Difference between revisions of "2001 AMC 12 Problems"

## Problem 1

The sum of two numbers is $S$. Suppose $3$ is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers? $\text{(A)}\ 2S + 3\qquad \text{(B)}\ 3S + 2\qquad \text{(C)}\ 3S + 6 \qquad\text{(D)} 2S + 6 \qquad \text{(E)}\ 2S + 12$

## Problem 2

Let $P(n)$ and $S(n)$ denote the product and the sum, respectively, of the digits of the integer $n$. For example, $P(23) = 6$ and $S(23) = 5$. Suppose $N$ is a two-digit number such that $N = P(N)+S(N)$. What is the units digit of $N$? $\text{(A)}\ 2\qquad \text{(B)}\ 3\qquad \text{(C)}\ 6\qquad \text{(D)}\ 8\qquad \text{(E)}\ 9$

## Problem 3

The state income tax where Kristin lives is levied at the rate of $p%$ (Error compiling LaTeX. ! Missing $inserted.) of the first <dollar/> $28000$ of annual income plus$(p + 2)%$(Error compiling LaTeX. ! Missing$ inserted.) of any amount above <dollar/> $28000$. Kristin noticed that the state income tax she paid amounted to $(p + 0.25)%$ (Error compiling LaTeX. ! Missing \$ inserted.) of her annual income. What was her annual income? $\text{(A)}\,$<dollar/> $28000\qquad \text{(B)}\,$<dollar/> $32000\qquad \text{(C)}\,$<dollar/> $35000\qquad \text{(D)}\,$<dollar/> $42000\qquad \text{(E)}\,$<dollar/> $56000$