MathDB

12

Part of 2002 AMC 10

Problems(3)

Earl E. Bird

Source:

2/11/2008
Mr. Earl E. Bird leaves his house for work at exactly 8:00 A.M. every morning. When he averages 40 40 miles per hour, he arrives at his workplace three minutes late. When he averages 60 60 miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should Mr. Bird drive to arrive at his workplace precisely on time? <spanclass=′latex−bold′>(A)</span> 45<spanclass=′latex−bold′>(B)</span> 48<spanclass=′latex−bold′>(C)</span> 50<spanclass=′latex−bold′>(D)</span> 55<spanclass=′latex−bold′>(E)</span> 58 <span class='latex-bold'>(A)</span>\ 45 \qquad <span class='latex-bold'>(B)</span>\ 48 \qquad <span class='latex-bold'>(C)</span>\ 50 \qquad <span class='latex-bold'>(D)</span>\ 55 \qquad <span class='latex-bold'>(E)</span>\ 58
No Solution

Source:

2/27/2008
For which of the following values of k k does the equation \frac{x\minus{}1}{x\minus{}2}\equal{}\frac{x\minus{}k}{x\minus{}6} have no solution for x x? <spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 5 <span class='latex-bold'>(A)</span>\ 1 \qquad <span class='latex-bold'>(B)</span>\ 2 \qquad <span class='latex-bold'>(C)</span>\ 3 \qquad <span class='latex-bold'>(D)</span>\ 4 \qquad <span class='latex-bold'>(E)</span>\ 5
Which Equals our Result?

Source:

4/2/2013
For fn(x)=xnf_n(x)=x^n and a≠1a\neq 1 consider
I. (f11(a)f13(a))14(f_{11}(a)f_{13}(a))^{14}
II. f11(a)f13(a)f14(a)f_{11}(a)f_{13}(a)f_{14}(a)
III. (f11(f13(a)))14(f_{11}(f_{13}(a)))^{14}
IV. f11(f13(f14(a)))f_{11}(f_{13}(f_{14}(a)))
Which of these equal f2002(a)f_{2002}(a)?
<spanclass=′latex−bold′>(A)</span>I and II only<spanclass=′latex−bold′>(B)</span>II and III only<spanclass=′latex−bold′>(C)</span>III and IV only<spanclass=′latex−bold′>(D)</span>II, III, and IV only<spanclass=′latex−bold′>(E)</span>all of them<span class='latex-bold'>(A) </span>\text{I and II only}\qquad<span class='latex-bold'>(B) </span>\text{II and III only}\qquad<span class='latex-bold'>(C) </span>\text{III and IV only}\qquad<span class='latex-bold'>(D) </span>\text{II, III, and IV only}\qquad<span class='latex-bold'>(E) </span>\text{all of them}