Is x|y|y^2 ?

Question

Is  x|y|>y^2 ?

1)  \frac{1}{y} + x^2 >3 
2)  x > |y|

GMATbuster's Collection

Archit3110 · Answer

#1
 \frac{1}{y} + x^2 >3 
x^2y>3y-1
if x= -1 , y=-2
-2>-7 but  x|y|>y^2  NO
if x=5 and y=5
then x^2y>3y-1 ; 5^3>14 ; yes but  x|y|>y^2  ; we get NO since 25=25
if x=10 and y=5
500>14 ; and 50>25 YES 
insufficient
#2
  x >l yl 
for any value of y be it + or -ve x>y so 
no unique value can we get to determine  x|y|>y^2   x|y|>y^2 ; sufficient
but for y=0 we get no value so insufficient
from 1&2 x>y sufficient
IMO C

Mohammadtaghikian · Answer

Answer is E
1)is not sufficient as we have x^2 which is clearly irrelevant
2)is not sufficient as y<x is not enough to prove the expression,we need to have y-<x as well
Both together is insufficient

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colinlin1 · Answer

B is sufficient

Since x>|y|>0, we multiply a positive number |y| to both ends get x|y|>|y||y|>0
|y||y|=y2
So x|y|>y2

GMATBusters · Answer

Is x|y|>y^2 ?
or Is x|y|>|y|^2 
or, Is |y|(x-|y|)>0?

Statement 1. 
 \frac{1}{y} + x^2 >3 
There can be infinite solutions to this inequality. it is clearly not sufficient. 
 NOT SUFFICIENT.
 
Statement 2:
 x > |y|  or x-|y|>0
this looks very similar to question stem Is |y|(x-|y|)>0?, 
so one tends to mark the answer as B.
Here is the  trap , If y = 0, then Is |y|(x-|y|)>0? would be NO, if y is not equal to 0, Is |y|(x-|y|)>0? is YES.
Hence Statement 2 is also  NOT SUFFICIENT.

Combining statement 1 & 2, 
St 1 gives a clue that y is not equal to 0, if y had been 0, then  \frac{1}{y} would be undefined.
Hence y is not equal to 0, Also, from st 2 x-|y|>0
hence |y|(x-|y|)>0? is also true, and we get a definite answer YES.

SUFFICIENT

So the answer is C

Is x|y|>y^2 ?

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