Inequality Madness

[heshamelaziry]

Is x > y ?

(1) -4x + 2y < y - 3x

(2) wx > wy


In statement 2, why can't I divide each side by w and get x > y ??????????????

[sanjana]

Statement 1
-----------

2y-y < -3x+4x
y<x - sufficient.

Statement 2
------------

wx-wy > 0
w(x-y) > 0

Now either W>0 and X-Y > 0 ==> X>Y
or W<0 and X-Y < 0 ==> X<Y

Hence the answer could be yes or no.
Insufficient.

IMO : A

Whats the OA?

[heshamelaziry]

Statement 1
-----------

2y-y < -3x+4x
y<x - sufficient.

Statement 2
------------

wx-wy > 0
w(x-y) > 0

Now either W>0 and X-Y > 0 ==> X>Y
or W<0 and X-Y < 0 ==> X<Y

Hence the answer could be yes or no.
Insufficient.

IMO : A

Whats the OA?[/quot


In statement 2, why can't I divide each side by w and get x > y ??????????????

OA is A. how you figure to do it this way rather than what I am describing above that is correct too !!!!!!!!!!!!!!

[regor60]

Simple reason can't divide by w. Assume w=-3 and x=-2, y=1 so

wx>wy = (-3)*(-2)> (-3)*(1) TRUE

divide by w

x>y = -2>1 FALSE

[aakar]

Just make a note to remember that in inequalities you can't multiple or divide by a variable, because the variable could be negative and could potentially flip the greater/less then sign.

[sanjana]

In Inequalities you should never divide by a number unless you know the sign of the number.

Also Suppose you have a normal equation
say,
X^2-X = 0

if you divide by x you get,
x-1=0,hence x=1
By doing this you have missed one solution of the equation completely,i.e x=0
You should always do,
x(x-1)=0
hence,x=0 or x=1.

Hope this helps!