AB is a two-digit number, with A representing the tens digit and B representing the unit digit, where A ≠ 0 and B ≠ 0. If the difference of AB and its converse equals 54, what could A+B equal?

GRE Quant Problem Solving
1

I am unable to understand the “converse” side of the problem . Is is A-B = 45 and B-A = 54 ? Could someone help me coming to the solution here ?

2

Hii Welcome to the club!!!
Since A is in the tens place and B is in units place in the initial AB its 10A+B
it’s (10A+B)-(10B+A)=54
A-B=6
since A and B had to be positive integers choose numbers for A>6 and B>0
for example A=7 and B=1 so it satisfies A-B=6 similarly you need to find the other pairs