Difference between revisions of "2015 AMC 12B Problems/Problem 25"

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==Problem==
 
==Problem==
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A bee starts flying from point <math>P_0</math>. She flies <math>1</math> inch due east to point <math>P_1</math>. For <math>j \ge 1</math>, once the bee reaches point <math>P_j</math>, she turns <math>30^{\circ}</math> counterclockwise and then flies <math>j+1</math> inches straight to point <math>P_{j+1}</math>. When the bee reaches <math>P_{2015}</math> she is exactly <math>a \sqrt{b} + c \sqrt{d}</math> inches away from <math>P_0</math>, where <math>a</math>, <math>b</math>, <math>c</math> and <math>d</math> are positive integers and <math>b</math> and <math>d</math> are not divisible by the square of any prime. What is <math>a+b+c+d</math> ?
  
 
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<math>\textbf{(A)}\; ? \qquad\textbf{(B)}\; ? \qquad\textbf{(C)}\; ? \qquad\textbf{(D)}\; ? \qquad\textbf{(E)}\; ?</math>
  
 
==Solution==
 
==Solution==

Revision as of 13:31, 3 March 2015

Problem

A bee starts flying from point $P_0$. She flies $1$ inch due east to point $P_1$. For $j \ge 1$, once the bee reaches point $P_j$, she turns $30^{\circ}$ counterclockwise and then flies $j+1$ inches straight to point $P_{j+1}$. When the bee reaches $P_{2015}$ she is exactly $a \sqrt{b} + c \sqrt{d}$ inches away from $P_0$, where $a$, $b$, $c$ and $d$ are positive integers and $b$ and $d$ are not divisible by the square of any prime. What is $a+b+c+d$ ?

$\textbf{(A)}\; ? \qquad\textbf{(B)}\; ? \qquad\textbf{(C)}\; ? \qquad\textbf{(D)}\; ? \qquad\textbf{(E)}\; ?$

Solution

See Also

2015 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 24
Followed by
Last Problem
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

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