Difference between revisions of "1992 AJHSME Problems/Problem 3"
5849206328x (talk | contribs) (Created page with '==Problem== What is the largest difference that can be formed by subtracting two numbers chosen from the set <math>\{ -16,-4,0,2,4,12 \}</math>? <math>\text{(A)}\ 10 \qquad \te…') |
|||
| Line 14: | Line 14: | ||
{{AJHSME box|year=1992|num-b=2|num-a=4}} | {{AJHSME box|year=1992|num-b=2|num-a=4}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 00:08, 5 July 2013
Problem
What is the largest difference that can be formed by subtracting two numbers chosen from the set 
?
Solution
To maximize anything of the form 
, we maximize 
and minimize 
. The maximal element of the set is 
and the minimal element is 
, so the maximal difference is
![\[12-(-16)=28\rightarrow \boxed{\text{D}}.\]](http://latex.artofproblemsolving.com/4/1/3/4130909a3cf950d7c81705d012d16db74a7e91d2.png)
See Also
| 1992 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
