A Single Digit Difference
Algebra
Level
2
If we take a certain 2-digit integer and reverse its digits to form another 2-digit integer, the absolute difference between these two numbers is a single digit.
What is this single digit?
The answer is 9.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Let the number be 1 0 x + y ......(1)
then its reverse is 1 0 y + x ......(2)
subtracting (2) from (1) we get,
1 0 x + y − ( 1 0 y + x ) = 9 x − 9 y = 9 ( x − y ) .
thus the difference of the two numbers is divisible by 9.