Difference between revisions of "1984 AIME Problems"
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== Problem 5 == | == Problem 5 == | ||
+ | Determine the value of <math>ab</math> if <math>\log_8a+\log_4b^2=5</math> and <math>\log_8b+\log_4a^2=7</math>. | ||
[[1984 AIME Problems/Problem 5|Solution]] | [[1984 AIME Problems/Problem 5|Solution]] |
Revision as of 22:42, 20 January 2007
Contents
[hide]Problem 1
Find the value of if , , is an arithmetic progression with common difference 1, and .
Problem 2
The integer is the smallest positive multiple of such that every digit of is either or . Compute .
Problem 3
A point is chosen in the interior of such that when lines are drawn through parallel to the sides of , the resulting smaller triangles , , and in the figure, have areas , , and , respectively. Find the area of .
Problem 4
Let be a list of positive integers - not necessarily distinct - in which the number appears. The arithmetic mean of the numbers in is . However, if is removed, the arithmetic mean of the numbers is . What's the largest number that can appear in ?
Problem 5
Determine the value of if and .