Difference between revisions of "2008 iTest Problems/Problem 15"
Coolmath34 (talk | contribs) (Created page with "==Problem== How many four-digit multiples of <math>8</math> are greater than <math>2008</math>? ==Solution== We can make a list of four-digit multiples of <math>8</math> that...") |
Rockmanex3 (talk | contribs) (Corrected math error) |
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| Line 7: | Line 7: | ||
<cmath>252, 253, 254, ..., 1248, 1249</cmath> | <cmath>252, 253, 254, ..., 1248, 1249</cmath> | ||
Now subtract <math>251</math> from every member of the list. | Now subtract <math>251</math> from every member of the list. | ||
| − | <cmath>1, 2, 3, ..., 998, | + | <cmath>1, 2, 3, ..., 998, 998</cmath> |
| − | There are <math> | + | There are <math>998</math> numbers in this list, so there are <math>\boxed{998}</math> four-digit multiples of <math>8</math> that are greater than <math>2008.</math> |
*Feel free to edit answer if this is not correct, but do not edit the process. | *Feel free to edit answer if this is not correct, but do not edit the process. | ||
| + | |||
| + | ==See Also== | ||
| + | {{2008 iTest box|num-b=14|num-a=16}} | ||
| + | |||
| + | [[Category:Introductory Number Theory Problems]] | ||
Latest revision as of 12:25, 22 June 2018
Problem
How many four-digit multiples of 
are greater than 
?
Solution
We can make a list of four-digit multiples of that are greater than 
The smallest multiple of that is larger than is 
so we can start with 
The largest four-digit multiple of 8 is 
![\[2016, 2024, 2032, ..., 9984, 9992\]](http://latex.artofproblemsolving.com/5/e/3/5e30b0eb8a2834729669204256c6e23306db53f9.png)
Divide everything in the list by 
![\[252, 253, 254, ..., 1248, 1249\]](http://latex.artofproblemsolving.com/1/c/8/1c8e357d93239eaa1fbb7d67ec115ac22587e38b.png)
Now subtract 
from every member of the list.
![\[1, 2, 3, ..., 998, 998\]](http://latex.artofproblemsolving.com/f/9/e/f9e8501c2681e9d37a8a66757221aa6294114084.png)
There are 
numbers in this list, so there are 
four-digit multiples of that are greater than
- Feel free to edit answer if this is not correct, but do not edit the process.
See Also
| 2008 iTest (Problems) | ||
| Preceded by: Problem 14 |
Followed by: Problem 16 | |
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