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Some doubt on Inequalities

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Senior Manager
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Joined: 08 Jan 2009
Posts: 326

Kudos [?]: 175 [0], given: 5

Some doubt on Inequalities [#permalink]

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New post 18 Feb 2009, 23:49
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Guys,

i was reading through the Basic Maths principles in the GMAT club and i came across this.I am really weak in inequalities and i require your help.

If x>-4 and y<-2 then x/y<2 . I know this condition is true.I substitute values and found it to be true.What confuses me is how to arrive at that conclusion ( x/y<2) quickly. What would be the Sign of the inequalities because substituion takes time.

I hope i got my question right to you.Please help

There was this one also .
If x<-4, y<2, then -x>4, y<2, -x/y>2, x/y<-2

if i take X = -6 and y = -3 then the condn does not satisfy.Am i missing out something.



From the Basic Maths Principles:
-----------------------------------------------------------------------------
Deal with negative numbers:
-a<-b<0, -c<-d<0
Then
-a-c<-b-d<0
-a-(-d)<-b-(-c)
However the sign needs to be flipped one more time if you are doing multiplication or division (because you are multiplying/dividing a negative number):
(-a)*(-c)>(-b)*(-d)
(-a)/(-d)>(-b)/(-c)

For example:
If x<-4, y<-2, we know that xy>8, but we don't know how x/y compare to (-4)/(-2)=2 since you can only do division when their signs are in different directions
If x>-4 and y<-2 then x/y<2 but we don't know how xy is compared to 8 since we can only do multiplication when their signs are the same direction.

It is easier to do the derivation, though, if you first change them to postive. For example:
If x<-4, y<-2, then -x>4, -y>2, xy>8
If x<-4, y<2, then -x>4, y<2, -x/y>2, x/y<-2
----------------------------------------------------------------------------------------------------------------------

Kudos [?]: 175 [0], given: 5

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Re: Some doubt on Inequalities [#permalink]

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New post 19 Feb 2009, 21:36
tkarthi4u wrote:
If x>-4 and y<-2 then x/y<2 . I know this condition is true.I substitute values and found it to be true.What confuses me is how to arrive at that conclusion ( x/y<2) quickly. What would be the Sign of the inequalities because substituion takes time.

I hope i got my question right to you.Please help

There was this one also.
If x<-4, y<2, then -x>4, y<2, -x/y>2, x/y<-2

if i take X = -6 and y = -3 then the condn does not satisfy. Am i missing out something.


Here you are changing only x to -x but not y to -y. you have to change both. If you are changing the sign of one variable, change the sign of another too.

If x < -4, and y < 2, then -x > 4, -y > -2. If so, -x/-y > -2. This inequality turns, finally, into 2 > x/y or x/y < 2, which is same as before.

I might have typos. Correct me if any.
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Kudos [?]: 834 [0], given: 19

Re: Some doubt on Inequalities   [#permalink] 19 Feb 2009, 21:36
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