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2014 AMC 12B Problems

Revision as of 22:41, 8 February 2014 by Dragon6point1 (talk | contribs) (Problem 14)

Problem 1

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Problem 2

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Problem 3

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Problem 4

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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

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Problem 11

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Problem 12

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Problem 13

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Problem 14

Amy, Bob, Charlie, Dorothy, Edd, and Frank each select distinct integers between $1$ and $100$, inclusive. What is the probability that the four integers are the lengths of the sides and diagonals of a cyclic quadrilateral?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ \frac{1}{42} \qquad \textbf{(C)}\ \frac{1}{30} \qquad \textbf{(D)}\ \frac{1}{21} \qquad \textbf{(E)}\ \frac{1}{7}$

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Let $S$ be the set of points on the graph of $y = x + \sqrt{x}$ such that $x$ is an integer between $-100$ and $100$, inclusive. How many distinct line segments with endpoints in $S$ have integer side lengths?

$\mathrm {(A) } 0 \qquad \mathrm {(B) } 1 \qquad \mathrm {(C) } 2 \qquad \mathrm {(D) } 3 \qquad \mathrm {(E) } 4$

Solution

Problem 18

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Problem 19

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Problem 20

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Problem 21

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Problem 22

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Problem 23

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Problem 24

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Problem 25

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