Difference between revisions of "2015 AMC 12B Problems/Problem 25"
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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> ? | 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> ? | ||
| − | <math>\textbf{(A)}\; | + | <math>\textbf{(A)}\; 2016 \qquad\textbf{(B)}\; 2024 \qquad\textbf{(C)}\; 2032 \qquad\textbf{(D)}\; 2040 \qquad\textbf{(E)}\; 2048</math> |
==Solution== | ==Solution== | ||
Revision as of 17:10, 3 March 2015
Problem
A bee starts flying from point 
. She flies 
inch due east to point 
. For 
, once the bee reaches point 
, she turns 
counterclockwise and then flies 
inches straight to point 
. When the bee reaches 
she is exactly 
inches away from , where 
, 
, 
and 
are positive integers and and are not divisible by the square of any prime. What is 
?
Solution
See Also
| 2015 AMC 12B (Problems • Answer Key • Resources) | |
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
