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 z an integer?

(1) 2z is an even number.

(2) 4z is an even number.

In the original condition we have 1 variable (z) and thus we need 1 equation to match the number of variables and equations. Since there is 1 each in 1) and 2), there is high probability that D is the answer.

In case of 1), 2z=even=2m(m is some integer), z=m therefore the answer is yes and the condition is suffi

In case of 2), 4z=even=2n(n is some integer), z=n/2, 4z=2, z=1/2 the answer is no, while for 4z=4, z=1 the answer is yes. Therefore the condition is not sufficient

Therefore the answer is A.

Normally 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 D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.

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