If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 54. By how much do the two digits differ?
Choose the correct choice
A) 3	B) 4	C) 5	D) 6	E) 7
Let’s first label the original two-digit integer as N. We can then say that N = 10A + B, where A is the tens digit and B is the units digit of N.   If this is hard to see let’s try it with a sample number, say 24. We can say the following:   24 = (2 x 10) + 4   24 = 20 + 4   24 = 24   Getting back to the problem, we are given that if the integer N has its digits reversed the resulting integer differs from the original by 54. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.   10B + A = reversed integer   Since we know the resulting integer differs from the original by 54 we can say:   10B + A – (10A + B) = 54   10B + A – 10A – B = 54   9B – 9A = 54   B – A = 6   Since B is the tens digit and A is the units digit, we can say that the digits differ by 6.   The answer is 6.
<result>D</result>
If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 54. By how much do the two digits differ?