2014 AMC 8 Problems/Problem 22
Contents
Problem 22
A -digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the units digit of the number?
Video Solution
https://youtu.be/7an5wU9Q5hk?t=2226
https://www.youtube.com/watch?v=RX3BxKW_wTU
Video Solution for Problems 21-25
https://www.youtube.com/watch?v=6S0u_fDjSxc
Solution
We can think of the number as , where a and b are digits. Since the number is equal to the product of the digits (
) plus the sum of the digits (
), we can say that
. We can simplify this to
, which factors to
. Dividing by
, we have that
. Therefore, the units digit,
, is
Solution 2
A two digit number is namely , where
and
are digits in which
and
. Therefore, we can make an equation with this information. We obtain
. This is just
Moving
and
to the right side, we get
Cancelling out the
s, we get
which is our desired answer as
is the second digit. Thus the answer is
.
~mathboy
See Also
2014 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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 AJHSME/AMC 8 Problems and Solutions |
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