Great explanation, abishekg21!
One other note on this one - if you didn't see a way to think it through algebraically and had to make a quick decision, another way to think this particular problem through is to look at the constraints:
You need two 2-digit numbers to sum to the answer choices:
181
165
121
99
44
Your range of potential 2-digit numbers is between 11 and 99 (10 doesn't work because the inverse would be 01, a one-digit number), so the range of sums is going to be between 22 and 198, with quite a few possibilities to sum 2-digit numbers toward the middle of that range but very few opportunities to hit at the ends (the only way to get 22 is 11 and 11; the only way to get 198 is 99 and 99).
So you may want to start at the ends because there are fewer combinations of 2-digit numbers (independent of the inverse digits) to even try to add to those numbers. 44 should be easy to spot - 22 + 22, but 181 requires:
A max of 99, meaning that the minimum second value is 82.
So you'd have to use the digits 8 and 9 to even have a chance. Your only options are 88+88, 98+89, and 99+99, none of which work, so choice A is a pretty quick elimination.
Now, that may only work on this question, so I'd recommend being comfortable enough to use Abishek's algebraic way, too, but when you're dealing with sums/multiples/etc. it's certainly possible to limit your options by looking at the potential ranges of values, and often you can make quick decisions that way.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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