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

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Re: If wxyz ≠ 0, does wxyz = 1? (1) w = 1/x, y = 1/z (2) wx^2 = 1/xyz [#permalink]
Bunuel wrote:
If $$wxyz ≠ 0$$, does $$wxyz = 1$$?

(1) $$w = \frac{1}{x}$$, $$y = \frac{1}{z}$$

(2) $$wx^2 = \frac{1}{xyz}$$

Asked: If $$wxyz ≠ 0$$, does $$wxyz = 1$$?

(1) $$w = \frac{1}{x}$$, $$y = \frac{1}{z}$$
wx = 1 & yz = 1; waxy = 1
SUFFICIENT

(2) $$wx^2 = \frac{1}{xyz}$$
wx^3yz = 1
wxyz = 1/x^2
will depend on value of x
NOT SUFFICIENT

IMO A
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Re: If wxyz ≠ 0, does wxyz = 1? (1) w = 1/x, y = 1/z (2) wx^2 = 1/xyz [#permalink]

Solution

Step 1- Given and To find

Given
• wxyz ≠ 0
o This means none out of w, x, y, and z can be 0.
To find
• Is wxyz =1?

To find whether wxyz =1, we need some extra information. Let us move to analyse the statements

Step 2: Analysing individual statements

Statement 1: w = 1/x, y = 1/z.
• wxyz = w × x ×× y × z = (1/x) × x × (1/z) × z = 1
This statement is sufficient to find the answer.

Statement 2: wx2 = 1/xyz
• wx = 1/(x^2× y × z)
• wxyz = (1/(x^2× y × z)) × y × z
• wxyz = 1/y^2
Since we don’t know the value of y, we cannot say whether 1/y^2 = 1 or not.

Hence, option A is the correct answer.