If xy^2z

Question

If  xy^2z < 0 , then which one of the following statements must also be true?

I. xz < 0
II. z < 0
III. xyz < 0

(A) None 
(B) I only 
(C) III only 
(D) I and II 
(E) II and III

Source:   Nova GMAT  
Difficulty Level:   600

Archit3110 · Answer

for  xy^2z < 0  
either of x,z has to be -ve and y may or may not be -ve
so 
out of given options xz < 0 is always true
IMO B

Diya52 · Answer

xy^2z<0. y^2>0. So xz<0. Either x positive and y negative. Or x negative and y positive. 1. xz<0 (true as established) 2. Z<0 (cant say as x could be <0). 3. xyz<0. xz<0 but y could be positive or negative. Just because y^2 is positive doesn't mean y is positive. So xyz is negative if y is positive and xyz is positive if y is negative. Only 1 can be established. Ans B

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KSBGC · Answer

Given,

xy^2z < 0

y^2 >0

So, xz<0. It indicates that either x or z is negative.

y could be negative or positive.

xyz<0. not always true. it is true only if y is positive.

Thus, B is the correct answer.

AnirudhaS · Answer

xy^2z<0 this means xz<0, as y^2 is always > 0 xz<0, also means either x or z are negative, both not both. I: says exactly that II: z <0 only when x>0. So it is NOT a must be true condition III: xyz<0, only when y>0, but we do not have any information about y Answer: B

TestPrepUnlimited · Answer

y^2  is always positive so we can move it over to the right side and get  xz < 0 . Thus we can conclude x and z have opposite signs, and we don't know anything about y besides it is not 0.

I. Correct.
II. We only know x and z have opposite signs, therefore z can be positive or negative.
III. xz must be negative, but we don't know the sign of y so we don't know the sign of xyz.

So only I is always true.

Ans: B

If xy^2z < 0 , then which one of the following statements must also be

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