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ploting ranges

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by what? » Sat Jul 16, 2011 11:45 pm
i am having trouble understanding a concept in number line.

If we are given the equation
n^2-n-2<0
we can solve it to
(n+1)(n-2)<0

this should give us n<-1 or n<2.

but this is not correct. The correct limits we should get to are n>-1 or n<2.

The first set of solutions is obviously wrong because plugging in n=-5 is not true to condition.
I know I am just missing some silly point... in solving one of the solutions. so someone please help me with my ah-haa moment.
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by mirantdon » Sun Jul 17, 2011 2:00 am
Well again as a rule of thumb .

(x-a)(x-b)<0 ---> gives a solution x lies between a and b .

and
(x-a)(x-b)>0 --> gives a solution x<a UNION x>b..
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by sanju09 » Sun Jul 17, 2011 2:08 am
what? wrote:i am having trouble understanding a concept in number line.

If we are given the equation
n^2-n-2<0
we can solve it to
(n+1)(n-2)<0

this should give us n<-1 or n<2.

but this is not correct. The correct limits we should get to are n>-1 or n<2.

The first set of solutions is obviously wrong because plugging in n=-5 is not true to condition.
I know I am just missing some silly point... in solving one of the solutions. so someone please help me with my ah-haa moment.
If (n + 1)(n - 2)< 0, then this is possible only when n + 1 > 0 and n - 2 < 0

i.e. when n > -1 and n < 2

i.e. when -1 < n < 2.

Do not try otherwise, because when n + 1 < 0, n - 2 cannot be positive to prove (n + 1)(n - 2)< 0 as true.
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by GMATGuruNY » Mon Jul 18, 2011 3:13 am
what? wrote:i am having trouble understanding a concept in number line.

If we are given the equation
n^2-n-2<0
we can solve it to
(n+1)(n-2)<0

this should give us n<-1 or n<2.

but this is not correct. The correct limits we should get to are n>-1 or n<2.

The first set of solutions is obviously wrong because plugging in n=-5 is not true to condition.
I know I am just missing some silly point... in solving one of the solutions. so someone please help me with my ah-haa moment.
Here is a surefire way to determine where (n+1)(n-2)<0:

1. Determine the critical points.
The critical points are where (n+1)(n-2) = 0.
(n+1)(n-2) = 0 when n=-1 or n=2.

2. Test one value to the right and left of each critical point.
To test n<-1, plug n=-2 into (n+1)(n-2)<0:
(-2+1)(-2-2)<0
4<0.
Doesn't work.
n<-1 is NOT part of the range.

To test -1<n<2, plug n=0 into (n+1)(n-2)<0:
(0+1)(0 -2)<0
-2<0.
This works.
-1<n<2 is part of the range.

To test n>2, plug n=3 into (n+1)(n-2)<0:
(3+1)(3-2)<0
4<0.
Doesn't work.
n>2 is NOT part of the range.

Thus, (n+1)(n-2)<0 only when -1<n<2.
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by KRISH1985 » Mon Jul 18, 2011 9:05 pm
Very good method Mitch!! cheers!
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by what? » Wed Jul 20, 2011 10:58 am
Thanks Mitch!

Although this concept is now clear to me, I have started to have doubts regarding what else have I been messing up by just solving equations and not applying these verification techniques...sigh!
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