Difference between revisions of "1985 AHSME Problems/Problem 12"
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Revision as of 12:00, 5 July 2013
Problem
Let's write 
and 
as three distinct prime numbers, where 
is not a prime. Which of the following is the smallest positive perfect cube leaving 
as a divisor?
Solution
For a number of the form 
to be a perfect cube and a multiple of 
, 
and 
must all be multiples of 
, 
, 
, and 
. The smallest multiple of greater than is , the smallest multiple of greater than 
is , and the smallest multiple of greater than 
is 
. Therefore, the smallest such is 
.
See Also
| 1985 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
