Bunuel wrote:

Is z + z < z ?

(1) -4z > 4z

(2) z^3 < z^2

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.

The question is modified as follows.

2z < z ?

⇔ z < 0 ?

Condition 1)

-4z > 4z

⇔ 0 > 8z

⇔ 0 > z

It is same as the question.

Condition 1) is sufficient.

Condition 2)

z^3 < z^2

⇔ z^3 - z^2 < 0

⇔ z^2(z-1) < 0

⇔ z - 1 < 0 since z^2 > 0

⇔ z < 1

Since the range of the question does not include that of the condition 2), the condition 2) is not sufficient.

Therefore, the answer is A.

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