Difference between revisions of "1994 AHSME Problems/Problem 10"
(Created page with "==Problem== For distinct real numbers <math>x</math> and <math>y</math>, let <math>M(x,y)</math> be the larger of <math>x</math> and <math>y</math> and let <math>m(x,y)</math> be...") |
m (→Solution) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 4: | Line 4: | ||
<math> \textbf{(A)}\ a \qquad\textbf{(B)}\ b \qquad\textbf{(C)}\ c \qquad\textbf{(D)}\ d \qquad\textbf{(E)}\ e </math> | <math> \textbf{(A)}\ a \qquad\textbf{(B)}\ b \qquad\textbf{(C)}\ c \qquad\textbf{(D)}\ d \qquad\textbf{(E)}\ e </math> | ||
==Solution== | ==Solution== | ||
| + | We work thorough the equation step by step, simplifying as follows: | ||
| + | |||
| + | <cmath>\begin{align*}M(M(a,m(b,c)),m(d,m(a,e)))&=M(M(a,b),m(d,a))\\&=M(b,a)\\&=\boxed{\textbf{(B) }b}\end{align*}</cmath> | ||
| + | |||
| + | --Solution by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=200685 TheMaskedMagician] | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{AHSME box|year=1994|num-b=9|num-a=11}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 16:33, 9 January 2021
Problem
For distinct real numbers 
and 
, let 
be the larger of and and let 
be the smaller of and . If 
, then
![\[M(M(a,m(b,c)),m(d,m(a,e)))=\]](http://latex.artofproblemsolving.com/a/3/f/a3f7bdac9edf08a74252c9ed5a6ea4817ba05ecc.png)
Solution
We work thorough the equation step by step, simplifying as follows:
--Solution by TheMaskedMagician
See Also
| 1994 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
