Data Sufficiency

Provided x,y,z <>0.

If z.y < x.y

And if z<x , Does it necessarily mean that y >0.


Also, if y > 0 , Does it necessarily mean z<x

only why Y is positive, then Z can be greater than X.

robbie523 wrote:only why Y is positive, then Z can be greater than X.

Can you elaborate ?. Let me post the question

zy<xy Is y > 0
1. z<x


zy < xy . Is z<x
1. y >0

zy<xy Is y > 0
1. z<x


zy < xy . Is z<x
1. y >0

for the first one, stm 1 is insufficient to prove y>0, since nothing about y is given, only know Z<X, doesn't assure wether the inequality will be reversed or not. Y still could be negative and reverse the inequality sign


for the second one, stm 1 is sufficient, cuz Y is the key factor in reversing the inequality. if Y>0, that mean with or without why, the inequality won't reverse, therefore, assured Z<X

to prove something, you need to use the premise that's already given, and plug in the other factors later. to see it is yes or no!

to prove something right is very difficult, but to prove something wrong, is very easy, you only need one example!

yes.

If z.y < x.y

And if z<x ,
then Y must be >0


Also, if y > 0 ,
then z must be <x

z.y < x.y
=>zy-xy<0
=>y(z-x)<0

if y>0, z-x<0=>z<x
if y<0, z-x>0=>z>x