2001 AMC 12 Problems

Revision as of 14:06, 16 February 2008 by Brut3Forc3 (talk | contribs) (Problem 3)

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?

$\text{(A)}\ 2S + 3\qquad \text{(B)}\ 3S + 2\qquad \text{(C)}\ 3S + 6 \qquad\text{(D)} 2S + 6 \qquad \text{(E)}\ 2S + 12$

Solution

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 $N$?

$\text{(A)}\ 2\qquad \text{(B)}\ 3\qquad \text{(C)}\ 6\qquad \text{(D)}\ 8\qquad \text{(E)}\ 9$

Solution

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/>$56000$

Solution

Problem 4

Solution

Problem 5

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Problem 6

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Problem 7

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Problem 8

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Problem 9

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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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