Question 1197732
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The responses from the other tutors show good formal algebraic solutions.<br>
If a formal algebraic solution is not required and the speed of solving the problem is important (as on a timed competitive test), then this kind of problem can be solved quickly using this fact:<br>
The difference between a 2-digit number and the 2-digit number with the digits reversed is 9 times the difference of the digits.<br>
It is easy to show this.  If t and u are the tens and units digits of the original number, then the original number is 10t+u and the number with the digits reversed is 10u+t.  The difference between the two 2-digit numbers is<br>
(10t+u)-(10u+t)=9t-9u=9(t-u)<br>
So in this problem, with a difference of 18 between the two 2-digit numbers, we know the sum of the digits is 6 and the difference is 2.  Logical reasoning and/or simple arithmetic or algebra shows us the two digits are 2 and 4.<br>
Then, since the number with the digits reversed is larger, the original number is 24.<br>