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.
Is x between 0 and 1?
(1) -x < x^3
(2) x < x^2
There is only 1 variable (x), and 2 equations are given so there is high chance (D) will be our answer.
If the range of the question includes that of the condition, the condition is sufficient. We can use this to solve questions quickly and accurately.
The question asks whether 0<x<1
From condition 1, x^3+x>0, x(x^2+1)>0 (as x^2+1>0). From this we get x>0. This is insufficient as the range of the question does not include this range.
From condition 2, x^2-x>0 x(x-1)>0, --> x<0 or 1<x. The condition answers the question 'no', so this is sufficient.
The answer therefore becomes (B).
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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