For this kind of question try to find example/counter-example.
(x^4)(y^3)(z^7)<0, xyz<0?
1.y<0
All respect: (x^4)(y^3)(z^7)<0
y<0 then z>0 given x^4 is positive and we have to do (x^4)(y^3)(z^7)<0
If y=-1, z=1, x=1 then xyz<0
If y=-1, z=1, x=-1, then xyz>0
Insufficient
2.z>0
All respect: (x^4)(y^3)(z^7)<0
z>0 then y<0
We have the same conditions as for 1) (z>0 and y<0)
so it is also insufficient
1and 2 gives you y<0 and z>0 so it is exactly the same.... and insufficient
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x^4y^3z^7
Source: Beat The GMAT — Data Sufficiency |
The solution can be generalized as:
1. y<0
For the given condition to be true z>0 but x<0 or x>0.
If x<0 then xyz>0
else if x>0 then xyz<0
2. z>0
Implies y<0 from the given condition.
Again x<0 or x>0.
Which again gives xyz>0 or xyz<0
3. Combining the 2 cases doesn't help as x<0 or x>0
So answer is E.
1. y<0
For the given condition to be true z>0 but x<0 or x>0.
If x<0 then xyz>0
else if x>0 then xyz<0
2. z>0
Implies y<0 from the given condition.
Again x<0 or x>0.
Which again gives xyz>0 or xyz<0
3. Combining the 2 cases doesn't help as x<0 or x>0
So answer is E.
