2018 AMC 10B Problems/Problem 13
Contents
Problem
How many of the first numbers in the sequence
are divisible by
?
Solution
Note that for some odd
will suffice
. Each
, so the answer is
(AOPS12142015)
Solution 2
If we divide each number by , we see a pattern occuring in every 4 numbers.
. We divide
by
to get
with
left over. One divisible number will be in the
left over, so out answer is
.
See Also
2018 AMC 10B (Problems • Answer Key • Resources) | ||
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 | ||
All AMC 10 Problems and Solutions |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.