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forum.virtualchallengemeets.com • View topic - AMC 12A 2012 #8

AMC 12A 2012 #8

American Mathematics Contest & American Invitational Mathematics Examination. See for more information
Note:USAMO/IMO-level questions need to go in the Olympiad section.

AMC 12A 2012 #8

Postby nsguy1350 » Fri Jun 15, 2012 9:35 pm

An iterative average of the numbers 1, 2, 3, 4, and 5 is computed 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?
2013 District 1/Region:
NS - 319/355
MA - 340/332
CA - 294/287
SC - 344/292
CS - 212/124 (fail)
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Re: AMC 12A 2012 #8

Postby darksaber21 » Sat Jun 16, 2012 12:20 pm

So, they are basically saying this is how to find the average:
[unparseable or potentially dangerous latex formula]

The minimum number can be obtained with the following order:
[unparseable or potentially dangerous latex formula]

The maximum number can be obtained with the following order:
[unparseable or potentially dangerous latex formula]

It makes sense why when you actually do it. Anyway, so now you just perform the action for both sequences and find the difference between the mean of both:
First for the minimum:
[unparseable or potentially dangerous latex formula]

Now for the maximum:
[unparseable or potentially dangerous latex formula]

Now for the difference:
[unparseable or potentially dangerous latex formula]
Now I know the stakes, and I'm willing to show what I gots. I will see you all at state for the first and final time, so let's end the year with a bang! :)
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