If X*Y*Z0, is X* Y^2 * Z^3

Question

If X*Y*Z>0, is X* Y^2 * Z^30

thearch · Answer

I think the sign of x and z doesn't really matter because x remains x and the sign of z and z^3 is the same.
So we don't care about statement (2).
We need to know the sign of y because a square is always positive.
So if y<0 (statement A) then it is true that when we square y 
x*y^2*z^3 changes sign.

So I'd say (1)

banerjeea_98 · Answer

"A".

X*Y*Z > 0.......multipying both sides with Z^2......
X*Y*Z^3 > 0.....(Z^2 doesn't change the sign).....eq 1

state I......now if y<0......then if we multiply by Y on both sides of eq 1, we will have to change signs as Y<0

X*Y^2*Z^3 < 0......so ans is YES....suff

state II.....From eqn1....and as X > 0.....as we don't know the sign of Y, we can't determine if is X*Y^2*Z^3 > or < 0....insuff

ketanm · Answer

Let me try... (assumption '*' = multiplication and '^' = power of) X*Y*Z > 0, is possible only when 1) All X,Y,Z are positive 2) Two of them are negative, but third is positive For (X)*(Y^2)*(Z^3) < 0 Definitely Y^2 is always positive. So for the above condition to satisfy. either 1) X is negative and Z is positive (which will imply Z^3 is positive) 2) X is positive and Z is negative (which implies Z^3 is negative) Consider (1) if Y < 0, it implies that either X or Z are negative but not both.... hence we are not sure whether the (X)*(Y^2)*(Z^3) < 0 Consider (2) if X > 0, then Y and Z both are of same sign. this again does not gives us sufficient proof that (X)*(Y^2)*(Z^3) < 0 Combining both (1) and (2) If Y<0 and X>0, then definitely Z<0 (to make X*Y*Z > 0) Hence (X)*(Y^2)*(Z^3) < 0. Hence both (1) and (2) are required.

sandeeplalit · Answer

sorry ketan

but A is the answer.. try with any value for B.. +ve, -Ve.. results are the same..

ketanm · Answer

I realised what mistake I did....

Taking (1) if Y is negative, then X and Z will have opposite signs.... and since Y^2 is always positive, the sign of term (X* Y^2 * Z^3) depends on signs of X and Z (which are different). Hence this term will always be negative. 

With only (2), sign of Z is important which is not provided...hence no answer from (2)

Ketan

Marina · Answer

1 is sufficient and 2 is not sufficient , thus it is A

mdf2 · Answer

we valid that Y^2 will positive so to get the assumption right either x or z must be negative at the first place.

if Y<0 , then the assumption is valided , either z or x is <0 then A is sufficient

Vijo · Answer

A.

There are two cases possible for x.y.z>0

1) All 3 are +ve.
2) 1 +ve and 2 -ve


Now from I) If y<0 and xyz>0 then either of x and z are -ve. For xy^2.z^3, the sign of x or z which ever is -ve remains the same thus it is definitely -ve.

from II) x>0 doesn't effect it.

700Plus · Answer

A.

When x>0, 
There are two cases
1.both y and z should be positive. y^2*z^3 will be +ve. so, the whole equations will be +ve.
2.both y and z are -ve. y^2*z^3 will be -ve. so, the whole equations will be -ve.
So you cant tell whther it is positive or negative when x>0

If XYZ>0, is X* Y^2 * Z^3<0? (1) Y<0 (2) X>0

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If X*Y*Z>0, is X* Y^2 * Z^3<0? (1) Y<0 (2) X>0