Nice explanation, shovan85!
One thing to add to this one - if you'd like to try to solve these algebraically, there's a method for these "reverse the digits" type problems that uses pure algebra:
You can express any two-digit number as a sum of its tens digit plus its ones digit by remembering to multiply the tens by 10. For example, 45 is 4*10 + 5.
So if we want to say that flip-flopping the digits is the same as adding 45, we'd say that:
10x + y is the initial number (x is the tens digit and y is the units)
10y + x is the new number (now y is the tens digit and x is the units)
And by flip-flopping we're adding 45, so we'd have:
10x + y = 10y + x + 45
Combine like terms to get:
9x = 9y + 45
Divide by 9 to simplify:
x = y + 5
so we know that there's a difference of 5 between the digits, so we could have:
16 & 61
27 & 72
38 & 83
49 & 94
The only option that's here in the answer choices is 83, so that's correct.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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