1994 AJHSME Problems/Problem 20: Difference between revisions
No edit summary |
No edit summary |
||
| Line 22: | Line 22: | ||
==See Also== | ==See Also== | ||
{{AJHSME box|year=1994|num-b=19|num-a=21}} | {{AJHSME box|year=1994|num-b=19|num-a=21}} | ||
{{MAA Notice}} | |||
Revision as of 23:14, 4 July 2013
Problem
Let 
and 
be four different digits selected from the set
If the sum 
is to be as small as possible, then must equal
Solution
![\[\frac{W}{X} + \frac{Y}{Z} = \frac{WZ+XY}{XZ}\]](http://latex.artofproblemsolving.com/9/1/4/914fbb8336720d6bceff189dfc81868bda5f761e.png)
Small fractions have small numerators and large denominators. To maximize the denominator, let 
and 
.
![\[\frac{9W+8Y}{72}\]](http://latex.artofproblemsolving.com/a/c/4/ac476641187669bdc5c0780909ff690c015b388f.png)
To minimize the numerator, let 
and 
.
![\[\frac{9+16}{72} = \boxed{\text{(D)}\ \frac{25}{72}}\]](http://latex.artofproblemsolving.com/e/1/0/e105dc69796a462ef9e96074b271a017d99c513e.png)
See Also
| 1994 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
