Is \(yz > wz?\)
z(y-w)>0....
Two cases..
I. y>w, and z>0
II. y<w and z<0
So we are looking for either of the two cases...

1. \(y > w\)
If z>0, yes
If z<0, or z=0, no
Insufficient

2. \(z^3 < z\)
This happens when 0<z<1 or when z<-1
Insufficient

Combi Ned..
y>w..
If z<-1...yz<wz.....no
If 0<z<1....yz>wz....yes
Insufficient

E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

chetan2u Bunuel

By stmt 1 we get to know that y>w

But since we do not know anything about z we cannot say with certainty that y>z

Insuff

By stmt 2, we get the eqn of the form

z^3 -z < 0
(z-1) * z * (z+1) < 0

This is possible when z is negative

So by combining we get a definitive answer.


Where did i go wrong?

Posted from my mobile device

First inequality rearranged to yz - wz > 0 then z (y - w) > 0

Statement 1) tells us y > w and that can be rearranged to y - w > 0

z ( y - w) > 0 we know one part is > 0 but don't know about Z so insufficient.

For Statement 2)

\(z^3 < z\) can be rearranged to \(z > z^3\) then \(z - z^3 > 0\) then \(z (1 - z^2) > 0\)

we know \(z > 0\) and \(1 - z^2\) can be rearranged to square of a difference \((1 - z) (1 + z) > 0\)

so 1 > z and 1 > - z so -1 < z

0 < z < 1 and z > - 1

since we have no information on (y-w) we cannot tell.

Insufficient.

Now combine both.

we know from first statement (y-w) is positive.

We also know from second statement that z can be positive or negative for example z can be 1/2 or -1/2

Insufficient.

Answer choice E