Difference between revisions of "2014 AMC 12B Problems"

(Problem 14)
(Problem 17)
Line 83: Line 83:
 
==Problem 17==
 
==Problem 17==
  
 +
Let <math>S</math> be the set of points on the graph of <math>y = x + \sqrtx</math> such that <math>x</math> is an integer between <math>-100</math> and <math>100</math>,  inclusive. How many distinct line segments with endpoints in <math>S</math> have integer side lengths?
 +
 +
<math>\mathrm {(A) } 0 \qquad \mathrm {(B) } 1 \qquad \mathrm {(C) } 2 \qquad \mathrm {(D) } 3 \qquad \mathrm {(E) } 4</math>
  
 
[[2014 AMC 12B Problems/Problem 17|Solution]]
 
[[2014 AMC 12B Problems/Problem 17|Solution]]

Revision as of 22:36, 8 February 2014

Problem 1

Solution

Problem 2

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Amy, Bob, Charlie, and Dorothy each select distinct integers between $1$ and $10$, inclusive. What is the probability that the four integers are side lengths of a cyclic quadrilateral?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ \frac{1}{16} \qquad \textbf{(C)}\ \frac{1}{12} \qquad \textbf{(D)}\ \frac{1}{8} \qquad \textbf{(E)}\ \frac{1}{4}$

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Let $S$ be the set of points on the graph of $y = x + \sqrtx$ (Error compiling LaTeX. ! Undefined control sequence.) 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

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

Invalid username
Login to AoPS