Difference between revisions of "1997 AJHSME Problems/Problem 19"
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Revision as of 16:13, 31 July 2011
Problem
If the product 
, what is the sum of 
and 
?
Solution
Notice that the numerator of the first fraction cancels out the denominator of the second fraction, and the numerator of the second fraction cancels out the denominator of the third fraction, and so on.
The only numbers left will be in the numerator from the last fraction and 
in the denominator from the first fraction. (The will cancel with the numerator of the preceeding number.) Thus, 
, and 
.
Since the numerator is always one more than the denominator, 
, and 
, giving an answer of 
See also
| 1997 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
