Difference between revisions of "2001 AMC 10 Problems/Problem 6"
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the units digits <math> b </math> is <math> \boxed{\textbf{(E) }9} </math>. | the units digits <math> b </math> is <math> \boxed{\textbf{(E) }9} </math>. | ||
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Revision as of 16:06, 16 March 2011
Problem
Let and
denote the product and the sum, respectively, of the digits of the integer
. For example,
and
. Suppose
is a two-digit number such that
. What is the units digit of
?
Solution
Let . We want to find a number such that
.
If we subtract the quantity from both sides, we are left with
.
We can also divide both sides by a and we are left with
the units digits is
.