If wxyz ≠ 0, does wxyz = 1? (1) w = 1/x, y = 1/z (2) wx^2 = 1/xyz

The product of any set of numbers can be ONE in some specific cases only.

One – if all the numbers involved are equal to 1 or -1. While dealing with -1, be careful about the number of terms since there's a negative sign involved.

Two – if we have numbers and their reciprocals being multiplied together.

The question data says that the product of the numbers w, x, y and z is not equal to 0. This means that none of the values are equal to 0.

From statement I alone, we know that w and x are reciprocals; so are y and z. Therefore, the product of these numbers will be 1.
Statement I alone is sufficient. Answer options B, C and E can be eliminated. Possible answer options are A or D.

From statement II alone, w\(x^2\) = \(\frac{1}{xyz}\). Since we need to check if wxyz = 1, we can swap the terms and rewrite the equation above as, wxyz = \(\frac{1}{x^2}\).

wxyz will be equal to 1 depending on whether x is equal to 1/-1 or not. Therefore, statement II alone is insufficient to answer the question with a unique Yes or No.
Answer option D can be eliminated. The correct answer option is A.

Always focus on what you are trying to find in the question and try to rewrite the expression/equation to obtain what you want on the LHS.

Hope that helps!