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inequality graphical approach, what to shade? see inside ... [#permalink]
25 Sep 2013, 04:28

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Hey,

I was practicing some of the inequalities questions and saw a lot of you who are using graphical approach to solve inequlity are struggling with which region to shade(or which region is green/true) ..

i don't know how to add attachments so will be just writing and using the examples nach used.

1. 3x+4y<3: take origin as reference .. point ... put it in the above inequality i.e. x=0 and y=0, it'll give you 0<3 which is true hence we'll shade the are which contains origin

2. -2x+5y<-3 take origin as reference and you'll get 0<-3 which is not true .. hence shade the area which does not contain origin .. its that simple ..

Re: inequality graphical approach, what to shade? see inside ... [#permalink]
25 Sep 2013, 05:56

Here is one example .. I guess I figured out how to add attachments:

Ques. is x negative?

1. x+y=-12 2. y-x<-12

Here it is:

Attachment:

example1.jpg [ 51.88 KiB | Viewed 758 times ]

1. draw the line x+y=-12 points on this line have both x +ve and -ve .. hence insufficient

2. draw line y-x=-12, put x=y=0(origin as reference) in inequality you'll get 0<-12 which is not true hence shade the region which doesn't contain origin(the dark green one) .. this region also contains value of x both +ve and -ve ..

1 and 2 we get the part of the light green line that is in dark green area and in this region x is +ve, hence sufficient ... answer is C

Thats a crappy jpg, I know .. :p

will post more of these if anyone would like to see _________________

4. Are x and y both positive? (1) 2x-2y=1 (2) x/y>1

here:

Attachment:

example2.jpg [ 71.28 KiB | Viewed 751 times ]

1. 2x-2y=1, draw it in x-y plane it passes through three quadrants hence we cannot say both x and y are +ve or not

2. x/y>1, here i took reference point as 0,1 it came 0>1 which is not true, lines which passes through are a bit spcial so we dont just shade the are which doesnt contain the reference point but shade the region between axis and line like I did in above paint-file

1+2 >> both lines are parallel and wont meet far far away in any quadrant .. the light green line in dark green region is the common portion and both x and y will be +ve in this region .. hence answer is C _________________

Forget Kudos ... be an altruist

gmatclubot

Re: inequality graphical approach, what to shade? see inside ...
[#permalink]
25 Sep 2013, 06:34

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