What is the greatest common divisor of positive integers m a

[Max@Math Revolution]

[GMAT math practice question]

What is the greatest common divisor of positive integers m and n?

1) m and n are consecutive
2) m^2 - n^2 = m + n

[Max@Math Revolution]

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Condition 1)
The gcd of two consecutive integers is always 1.
Thus, condition 1) is sufficient.

Condition 2)
If m^2-n^2 = m+n, then (m+n)(m-n)=m+n and m-n = 1 since m+n ≠ 0.
This implies that m and n are consecutive integers, and their gcd is 1.
Condition 2) is sufficient since it yields a unique answer.

Therefore, D is the answer.
Answer: D

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.