2008 iTest Problems/Problem 15

Problem

How many four-digit multiples of $8$ are greater than $2008$?

Solution

We can make a list of four-digit multiples of $8$ that are greater than $2008.$ The smallest multiple of $8$ that is larger than $2008$ is $2016,$ so we can start with $2016.$ The largest four-digit multiple of 8 is $9992.$ \[2016, 2024, 2032,  ..., 9984, 9992\] Divide everything in the list by $8:$ \[252, 253, 254, ..., 1248, 1249\] Now subtract $251$ from every member of the list. \[1, 2, 3, ..., 998, 998\] There are $998$ numbers in this list, so there are $\boxed{998}$ four-digit multiples of $8$ that are greater than $2008.$

  • 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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