Data sufficiency inequality question

[guy.b]

Hi,
The DS question below is from MAN CAT exam. I didn't find it in another thread.

Is x·|y| > y^2?
(1) x > y
(2) y > 0

It is extremely tempting to divide both sides of this inequality by y or by the |y|, to come up with a rephrased question of "is x > y?" However, we do not know the sign of y, so this cannot be done.

I do not understand the explaination above.
why is ti wrong to divide both sides by |y| which is positive. Then, the question is equivalent to
Is x > |y|?

[Dijkstras]

You can divide any inequality by positive number.There is nothing wrong in that.

[guy.b]

So is there a mistake in the official answer given by Manhattan Gmat below?

It is extremely tempting to divide both sides of this inequality by y or by the |y|, to come up with a rephrased question of "is x > y?" However, we do not know the sign of y, so this cannot be done

[mschwrtz]

No mistake, though apparently not quite clear enough.

What is y^2 divided by |y|?

If y>0, then |y|=y, so y^2 divided by |y|=y.

If y<0, then |y|=-y, so y^2 divided by |y|=-y.

Testing values will show that statement 1 is not sufficient, and so that simply dividing by |y| is wrong.

Is x·|y| > y^2?
(1) x > y

Suppose that y=-3 and x=2, then answer is no.
Suppose that y=1 and x=2, then answer is yes.
Not sufficient.

[yousuf_azim]

Dears,

What is the Ans?

[StaceyKoprince]

The answer is C.

[guduruaravind]

CASE 1 :x|y|> y^2
there are two cases
i)y>0
x.y>y^2
y(x-y)>0

from here we can say

if y>0 then (x-y)>0
y<0 then (x-y)<0

ii)y<0
-x.y-y^2>0
x.y+y^2<0
y(x+y)<0
from the options we can see that nothing is mentioned about x+y so there in no point in further evaluating this case.

CASE 2: x|y|<y^2

then proceesing similarly we get

y(x-y) < 0

i.e if y>0 (x-y)<0
y<0 (x-y)>0

from statement 1

we know (x-y)>0 this statement happens in both case 1 and case 2 . so not sufficient.

from statement 2

y>0.This happens in both case1 and case 2 . so not sufficient.

using statement 1 and 2

y>0 and (x-y)>0
this happens only in case 1 . so we can conclude that x|y|>y^2 using both the statements.

[tim]

there are a couple of mistakes here, but in general you've got the right idea..

[michail.palagaschwili]

Hi all, I've tried to solve this one comceptually. I don't think that the division by |y| is probematic because of the signs, because both |y| and y^2 are positive. I would say we don't know whether y=0, that's why we cannot just divide by y.

Question: x*|y| > y^2 --> x*|y| > |y| ? As |y| is ≥ 0, we have to find out two things: a) y=0 ? and b) x > 0
(1) x > y
y=-5, x=-2 -> NO, y=-5, x=2 -> Yes

(2) y > 0
Clearly not sufficient, because if x < 0 the answer is NO, if x > 0 the answer is YES

(1)+(2) x > y > 0 we have found both a and b (see question) --> y is not equal to zero, now, the whole expression depends only on the value of x, and as we have already tested in (1) if x > 0 the answer is YES.
Answer C

Please correct me if my reasoning was wrong. Thanks.

[RonPurewal]

Question: x*|y| > y^2 --> x*|y| > |y| ?

you didn't mean to have that red thing there, right?

like, you meant to just write "x > |y| ?"

if so, then, yes, your analysis is on point. (the rest of your analysis seems to be geared toward the question WITHOUT the red thing, as it should be.)