Difference between revisions of "2005 AMC 10A Problems/Problem 16"
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So the numbers that have this property are <math>40</math>, <math>41</math>, <math>42</math>, <math>43</math>, <math>44</math>, <math>45</math>, <math>46</math>, <math>47</math>, <math>48</math>, <math>49</math>. | So the numbers that have this property are <math>40</math>, <math>41</math>, <math>42</math>, <math>43</math>, <math>44</math>, <math>45</math>, <math>46</math>, <math>47</math>, <math>48</math>, <math>49</math>. | ||
| − | Therefore the answer is <math>10\Rightarrow (D)</math> | + | Therefore the answer is <math>10\Rightarrow</math> <math>(D)</math> |
==See Also== | ==See Also== | ||
Revision as of 16:27, 8 December 2020
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. 
