Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 13"
(New page: ==Problem== {{empty}} ==Solution== {{solution}} ==See also== {{CYMO box|year=2006|l=Lyceum|num-b=12|num-a=14}}) |
(sol) |
||
| Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
| − | { | + | The sum of the digits of the number <math>10^{2006}-2006</math> is |
| + | |||
| + | A. <math>18006</math> | ||
| + | |||
| + | B. <math>20060</math> | ||
| + | |||
| + | C. <math>2006</math> | ||
| + | |||
| + | D. <math>18047</math> | ||
| + | |||
| + | E. None of these | ||
==Solution== | ==Solution== | ||
| − | {{ | + | <math>10^{2006}</math> is a <math>1</math> followed by 2006 <math>0</math>s; when we subtract, we will get something approximately close to 2006 <math>9</math>s. The last four digits are <math>10000 - 2006 = 7994</math>, and so we have 2002 <math>9</math>s followed by <math>7994</math>. The sum of these is <math>2002 \cdot 9 + 7 + 9 + 9 + 4 = 18047 \Longrightarrow \mathrm{(D)}</math> |
==See also== | ==See also== | ||
{{CYMO box|year=2006|l=Lyceum|num-b=12|num-a=14}} | {{CYMO box|year=2006|l=Lyceum|num-b=12|num-a=14}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
Revision as of 18:23, 17 October 2007
Problem
The sum of the digits of the number 
is
A. 
B. 
C. 
D. 
E. None of these
Solution
is a 
followed by 2006 
s; when we subtract, we will get something approximately close to 2006 
s. The last four digits are 
, and so we have 2002 s followed by 
. The sum of these is 
See also
| 2006 Cyprus MO, Lyceum (Problems) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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 | ||
