2018 AMC 8 Problems/Problem 21
Problem 21
How many positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 5 when divided by 9, and a remainder of 7 when divided by 11?
Solution #1
Looking at the values, we notice that ,
and
. This means we are looking for a value that is four less than a multiple of
,
, and
. The least common multiple of these numbers is
, so the numbers that fulfill this can be written as
, where
is a positive integer. This value is only a three digit integer when
is
or
, which gives
and
respectively. Thus we have
values, so our answer is
:D
See Also
2018 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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