Inequality Madness

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Thu Oct 15, 2009 8:38 pm

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 ??????????????

Last edited by heshamelaziry on Thu Oct 15, 2009 10:06 pm, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Thu Oct 15, 2009 8:38 pm

sanjana: Master | Next Rank: 500 Posts; Posts: 182; Joined: Sun Aug 02, 2009 7:19 pm; Thanked: 18 times; GMAT Score:680

by sanjana » Thu Oct 15, 2009 9:35 pm

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?

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Thu Oct 15, 2009 10:05 pm

sanjana wrote: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 !!!!!!!!!!!!!!

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Fri Oct 16, 2009 5:52 am

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

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aakar: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Sep 02, 2009 6:06 am; Thanked: 1 times

by aakar » Fri Oct 16, 2009 5:59 am

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.

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sanjana: Master | Next Rank: 500 Posts; Posts: 182; Joined: Sun Aug 02, 2009 7:19 pm; Thanked: 18 times; GMAT Score:680

by sanjana » Fri Oct 16, 2009 7:25 am

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!

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