MathDB

13

Part of 2012 AMC 10

Problems(2)

Iterative Averages of the First Five Natural Numbers

Source: 2012 AMC 12A Problem #8 and AMC 10A Problem #13

2/8/2012
An iterative average of the numbers 11, 22, 33, 44, and 55 is computed in the following way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of that with the fourth number, and finally the mean of that with the fifth number. What is the difference between the largest and smallest possible values that can be obtained using this procedure?
<spanclass=′latex−bold′>(A)</span> 3116<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 178<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 6516 <span class='latex-bold'>(A)</span>\ \frac{31}{16}\qquad<span class='latex-bold'>(B)</span>\ 2\qquad<span class='latex-bold'>(C)</span>\ \frac{17}{8}\qquad<span class='latex-bold'>(D)</span>\ 3\qquad<span class='latex-bold'>(E)</span>\ \frac{65}{16}
AMC
Clea Walking Down Escalator

Source: 2012 AMC10B Problem #13

2/23/2012
It takes Clea 6060 seconds to walk down an escalator when it is not operating and only 2424 seconds to walk down the escalator when it is operating. How many seconds does it take Clea to ride down the operating escalator when she just stands on it?
<spanclass=′latex−bold′>(A)</span> 36<spanclass=′latex−bold′>(B)</span> 40<spanclass=′latex−bold′>(C)</span> 42<spanclass=′latex−bold′>(D)</span> 48<spanclass=′latex−bold′>(E)</span> 52 <span class='latex-bold'>(A)</span>\ 36\qquad<span class='latex-bold'>(B)</span>\ 40\qquad<span class='latex-bold'>(C)</span>\ 42\qquad<span class='latex-bold'>(D)</span>\ 48\qquad<span class='latex-bold'>(E)</span>\ 52
AMC