2013 AMC 10A Problems/Problem 13
Problem
How many three-digit numbers are not divisible by , have digits that sum to less than
, and have the first digit equal to the third digit?
Solution
These three digit numbers are of the form . We see that
and
, as
does not yield a three-digit integer and
yields a number divisible by 5.
The second condition is that the sum . When
is
,
,
, or
, y can be any digit from
to
, as
. This yields
numbers.
When , we see that
so
. This yields
more numbers.
When ,
so
. This yields
more numbers.
When ,
so
. This yields
more numbers.
When ,
so
. This yields
more numbers.
Summing, we get
See Also
2013 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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All AMC 10 Problems and Solutions |
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