Difference between revisions of "2001 AMC 12 Problems/Problem 2"
Pidigits125 (talk | contribs) (→See Also) |
Pidigits125 (talk | contribs) |
||
| Line 1: | Line 1: | ||
| + | {{duplicate|[[2001 AMC 12 Problems|2001 AMC 12 #2]] and [[2002 AMC 10A Problems|2002 AMC 10A #6]]}} | ||
| + | |||
== Problem == | == Problem == | ||
Let <math>P(n)</math> and <math>S(n)</math> denote the product and the sum, respectively, of the digits | Let <math>P(n)</math> and <math>S(n)</math> denote the product and the sum, respectively, of the digits | ||
Revision as of 15:37, 16 March 2011
- The following problem is from both the 2001 AMC 12 #2 and 2002 AMC 10A #6, so both problems redirect to this page.
Problem
Let 
and 
denote the product and the sum, respectively, of the digits
of the integer 
. For example, 
and 
. Suppose 
is a
two-digit number such that 
. What is the units digit of ?
Solution
Denote 
and 
as the tens and units digit of , respectively. Then 
. It follows that 
, which implies that 
. Since 
, 
. So the answer is 
.
See Also
| 2001 AMC 12 (Problems • Answer Key • Resources) | |
| Preceded by Problem 1 |
Followed by Problem 3 |
| 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 12 Problems and Solutions | |
| 2001 AMC 10 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 | ||
