Difference between revisions of "1985 AHSME Problems/Problem 5"
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Revision as of 11:59, 5 July 2013
Problem
Which terms must be removed from the sum
if the sum of the remaining terms is equal to 
?
Solution
First, we sum all of the terms to see how much more than the entire sum is.
So we want two of the terms that sum to 
.
Consider 
. Therefore, we must have 
as a factor of 
. Notice that 
is the only possible value of 
and 
that's a multiple of 
, so one of or must be . Now subtract 
, so the two fractions we must remove are 
.
See Also
| 1985 AHSME (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 • 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. 
