Is X^(a+b) > X^(a-b) if both a and b are positive integers?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are 3 variables and 0 equation. Thus the answer E is most likely.

\(x = 1\)
\(x^{a+b} = x^{a-b}\): The answer to the question is false.

\(x = 2, a =1, b =1\).
\(x^{a+b} > x^{a-b}\): The answer to the question is true.

Therefore, the answer is E as expected.


For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.