2008 iTest Problems/Problem 15
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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