Conceptual question

[madhur_ahuja]

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

[robbie523]

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

[madhur_ahuja]

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

[robbie523]

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!

[tohellandback]

yes.

If z.y < x.y

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


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

[scoobydooby]

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

[yezz]

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

from given

y<x-z is y>0

from 1

z-x<0 ie: x-z>0, using this info and plugging in the given

y<+ve doesnt imply that y is +ve...insuff

[Ian Stewart]

Can you elaborate ?. Let me post the question

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

If z < x, we can multiply on both sides by y. If y is negative, we'd need to reverse the inequality, so we'd get zy > xy. We know that's not true, however, because we're told in the stem that zy < xy. So y cannot be negative, and since y cannot be zero, y must be positive. So yes, your conclusion is correct, and Statement 1 is sufficient.

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

Since y is positive, we can divide by y on both sides of the inequality zy < xy without needing to reverse the inequality, so we find that z < x, and Statement 1 is sufficient.