Difference between revisions of "1987 AJHSME Problems/Problem 8"
5849206328x (talk | contribs) (New page: ==Problem== If <math>\text{A}</math> and <math>\text{B}</math> are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is <cmath>\...) |
5849206328x (talk | contribs) m |
||
| Line 24: | Line 24: | ||
==See Also== | ==See Also== | ||
| − | [[ | + | {{AJHSME box|year=1987|num-b=7|num-a=9}} |
| + | [[Category:Introductory Algebra Problems]] | ||
Revision as of 20:15, 27 May 2009
Problem
If 
and 
are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is
![\[\begin{tabular}[t]{cccc} 9 & 8 & 7 & 6 \\ & A & 3 & 2 \\ & & B & 1 \\ \hline \end{tabular}\]](http://latex.artofproblemsolving.com/0/9/a/09af7496b4ffdb27348f275b8ab9b58041caf217.png)
Solution
The minimum possible value of this sum is when 
, which is ![\[9876+132+11=10019\]](http://latex.artofproblemsolving.com/b/8/d/b8d9c5ff0d72788fd3bafee806fea3330f82d1b0.png)
The largest possible value of the sum is when 
, making the sum ![\[9876+999+91=10966\]](http://latex.artofproblemsolving.com/0/e/e/0eedd62a32ae123a5370e982d20466ed3062bcb6.png)
Since all the possible sums are between 
and 
, they must have 
digits.
See Also
| 1987 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 | ||
