carcass wrote:

Is 0 < y < 1 ?

(1) \(0 < \sqrt{y} < 1\)

(2) y^2=1/4

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 is 1 variable and 0 equation. Thus the answer is D most likely.

Condition 1)

Squaring all sides of the inequalities \(0 < \sqrt{y} < 1\), we have \(0 < y < 1\).

Thus this is sufficient.

Condition 2)

From \(y^2 = \frac{1}{4}\), we have \(y = \frac{1}{2}\) or \(y = -\frac{1}{2}\).

The answer is not unique. Hence this it not sufficient.

Therefore A is the answer.

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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