Answer:
Step-by-step explanation:
2005 AMC 8 Problems/Problem 20
Problem
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24$
Solution
Alice moves $5k$ steps and Bob moves $9k$ steps, where $k$ is the turn they are on. Alice and Bob coincide when the number of steps they move collectively, $14k$, is a multiple of $12$. Since this number must be a multiple of $12$, as stated in the previous sentence, $14$ has a factor $2$, $k$ must have a factor of $6$. The smallest number of turns that is a multiple of $6$ is $\boxed{\textbf{(A)}\ 6}$.
See Also
2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 19 Followed by
Problem 21
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 AJHSME/AMC 8 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
Answer: 198 ft^2
total Area = Area of rectangle + area of trapzoid
= base*height + .5(b1+b2)*height
9*18+.5(9+3)6
162+36
198
Answer:
$33.88
Step-by-step explanation:
12.1*2.8 is equal to $33.88
Answer:
$3,153.32
Step-by-step explanation:
Given that
The deposited amount is $3,000
The annual interest rate is 1.25%
So, the semi-annual interest rate is 1.25% ÷2 = 0.625%
And, the time period = 4 × 2 = 8
We need to find out the final balance
So,
As we know that
Future value = Present value × (1 + rate of interest)^number of years
= $3,000 × (1 + 0.625%)^8
= $3,153.32
Answer:
Wouldn't it be answer B?
Step-by-step explanation:
The rest of the answers have addition which is not in the problem provided.
