If xyz 0, is x(y^2)(z^3) 0 ? (1) y 0 (2) x 0

Question

If  xyz > 0 , is  x(y^2)(z^3) > 0  ?

(1)  y > 0 
(2)  x > 0

Chethan92 · Answer

Given  xyz > 0 . Means either all x, y, and z are positive or 2 of them are negative.

From 1:

y > 0 
 y^2  will always be positive. But value of x and z are unknown. Hence 1 is insufficient.

From 2:

x > 0 
x = +ve. But no info about y and z.
Hence 2 is insufficient.

Combining both
x and y are > 0. Then z has to be +ve. 
Hence  x(y^2)(z^3) > 0

C is the answer.

PgRaul · Answer

If xyz>0xyz>0, is x(y2)(z3)>0x(y2)(z3)>0 ?

(1) y>0
(2) x>0

1)y>0, no info abt x and z. Insufficient,

2)x>0
y^2 will be +ve, as square of any number is always positive
but no info on z. Insufficient

Combining both
x and y are > 0. Then z has to be +ve.
Hence x(y2)(z3)>0x(y2)(z3)>0

C is the answer.

Abir77 · Answer

Please enlighten me here
From (1) we get that Y>0 
That means X and Z both will be either positive or negative
If both are positive in that case x(y^2)(z^3) > 0 -----True
If both are negative in that case x(y^2)(z^3) > 0 -----True

So in my opinion 1 is sufficient.
Please correct my flaws

Gaurav2896 · Answer

Here option A is correct as ,if Y>0
then either a and z both are positive or both are negative as xyz >0.
In the both the conditions xy^2z^3 will be postiive.

CEdward · Answer

If xyz>0, is x(y^2)(z3)>0?

Since xyz > 0, there are two possibilities:
1. (+)(+)(+) OR
2. (+)(-)(-)

We need to see what happens to these scenarios given the ranges below.

(1) y>0
Scenario 1 checks out if all three are positive so x(y^2)(z3)>0
Scenario 2 checks out if y is positive, but x and z are negative so x(y^2)(z3)>0
Sufficient.

(2) x>0
Scenario 1 checks out if all three are positive so x(y^2)(z3)>0
Scenario 2 does not check out because y^2 ends up positive so you get (+)(+)(-) so x(y^2)(z3) <0.
Insufficient.

mserraba · Answer

xyz>0

Question: x(y^2)(z^3)>0 ??? as we know that x(y^2)(z^3) = xyz(yz^2), 
We can rephrase the Question as: xyz(yz^2)>0???

Given that xyz>0 (+) and z^2>0 (+) we only need to know the sign value of y.

Answer A

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If xyz > 0, is x(y^2)(z^3) > 0 ? (1) y > 0 (2) x > 0

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