1988 AIME Problems/Problem 5
Revision as of 19:11, 4 July 2013 by Nathan wailes (talk | contribs)
Problem
Let , in lowest terms, be the probability that a randomly chosen positive divisor of
is an integer multiple of
. Find
.
Solution
, so it has
factors. Out of these, we only want those factors of
which are divisible by
; it is easy to draw a bijection to the number of factors that
has, which is
. Our probability is
, and
.
See also
1988 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.