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 23:42, 20 January 2007
Contents
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
.