Difference between revisions of "2005 AMC 10A Problems/Problem 16"
Dairyqueenxd (talk | contribs) (→Solution) |
Partho saha (talk | contribs) m (→See Also) |
||
| Line 19: | Line 19: | ||
{{AMC10 box|year=2005|ab=A|num-b=15|num-a=17}} | {{AMC10 box|year=2005|ab=A|num-b=15|num-a=17}} | ||
| − | [[Category:Introductory | + | [[Category:Introductory Number Theory Problems]] |
[[Category:Area Ratio Problems]] | [[Category:Area Ratio Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 11:37, 10 August 2022
Problem
The sum of the digits of a two-digit number is subtracted from the number. The units digit of the result is 
. How many two-digit numbers have this property?
Solution
Let the number be 
where 
and 
are the tens and units digits of the number.
So 
must have a units digit of
This is only possible if 
, so 
is the only way this can be true.
So the numbers that have this property are 
.
Therefore the answer is 
See Also
| 2005 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
