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kevincan
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Does |x(x-2)(x+4)|= x^3+2x^2-8x ? (1) |x+2| < |x+1| (2) x 14 Jul 2006, 03:53
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Does |x(x-2)(x+4)|= x^3+2x^2-8x ?

(1) |x+2| -3



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Does |x(x-2)(x+4)|= x^3+2x^2-8x ? (1) |x+2| < |x+1| (2) x Updated on: 14 Jul 2006, 07:33
Originally posted by game over on 14 Jul 2006, 05:09.
Last edited by game over on 14 Jul 2006, 07:33, edited 1 time in total.
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(2) not sufficient, f. e. x=25 => both sides are equal; x=-2.5, RHS<0, LHS>0.

(1) is not sufficient

(1) is fulfilled, if x< -1.5
|x(x-2)(x+4)| = x(x-2)(x+4) if -4 <= x <= 0 and -x(x-2)(x+4) if x <=-4.

choose x=-2 or x=-5.

But using (2), we know that x>-3. => -3<x<-1.5
=> Both statements together are sufficient.
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Does |x(x-2)(x+4)|= x^3+2x^2-8x ? (1) |x+2| < |x+1| (2) x 14 Jul 2006, 07:04
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kevincan
Does |x(x-2)(x+4)|= x^3+2x^2-8x ?

(1) |x+2| < |x+1|
(2) x > -3
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|x(x-2)(x+4)|= x^3+2x^2-8x ?
|x^3+2x^2-8x|= x^3+2x^2-8x ?

1. x is not an integer, so x < -3/2. if x^3+2x^2-8x is -ve not otherwise yes. so nsf.
2. x could be +ve or -ve but if it is >-3, each side is equal. suff.

B.
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Does |x(x-2)(x+4)|= x^3+2x^2-8x ? (1) |x+2| < |x+1| (2) x 14 Jul 2006, 07:07
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kevincan
Does |x(x-2)(x+4)|= x^3+2x^2-8x ?

(1) |x+2| < |x+1|
(2) x > -3
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B

|x(x-2)(x+4)|= x^3+2x^2-8x can be written as

|x(x-2)(x+4)|= x(x-2)(x+4)............EQ1

EQ1 one will be true if all three terms are +ve or exactly two terms are -ve.: i.e x >= -4
EQ1 one will be false if all three terms are -ve or exactly 1 term is -ve: i.e x <-4

St1: This statement says x < -2. Stem can be true (x = -3) or false (x = -5): INSUFF

St2: x > -3 : Stem is always true: SUFF
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Does |x(x-2)(x+4)|= x^3+2x^2-8x ? (1) |x+2| < |x+1| (2) x 30 Aug 2006, 02:58
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kevincan
Does |x(x-2)(x+4)|= x^3+2x^2-8x ?

(1) |x+2| < |x+1|
(2) x > -3
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Hi guys just saw this I think the answer is suppose to be C not B

From the question stem |x(x-2)(x+4)|= x^3+2x^2-8x
if x(x-2)(x+4)>0 so obtaining the critical points
x<-4 -4<x<0 and 0<x<2 x>2
If x<-4 |x(x-2)(x+4)|<0
If -4<x<0 |x(x-2)(x+4)|>0
If 0<x<2 |x(x-2)(x+4)|<0
If x>2 |x(x-2)(x+4)|>0

From 1 using the same strategy we can determine that x<-2 insuff the expression can either be positive or negative

From 2 x>-3 insufficient expression can be positive or negative
combine -3<x<-2 sufficient
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Does |x(x-2)(x+4)|= x^3+2x^2-8x ? (1) |x+2| < |x+1| (2) x 09 Sep 2006, 21:07
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I get C as well....

is |x(x-2)(x+4)| = x(x-2)(x+4)??

LHS is always +ve, so we need to find out if x(x-2)(x+4) is +ve...

From 1:


|x+2| < |x+1|

Squaring both sides, we get....

x^2+4x+4 < x^2+2x+1
=> 2x < -3
or x < -1.5

This makes 'x' -ve
This makes '-x-2' -ve
This may make 'x+4' +ve or -ve....INSUFF

From 2:

x > -3

This means the 3rd term (x+4) is always +ve

At x= -2: (-2)(-2-2) +ve
At x = -1: (-1)(-3) +ve
At x= 0 0 ok
At x = 1: 1(-1) -ve.....INSUFF


Taking 1 and 2 together....
-3 < x < -1.5

The value is always +ve....
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Does |x(x-2)(x+4)|= x^3+2x^2-8x ? (1) |x+2| < |x+1| (2) x 13 Sep 2006, 13:34
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kevincan
Does |x(x-2)(x+4)|= x^3+2x^2-8x ?

(1) |x+2| < |x+1|
(2) x > -3
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Note that Q=x(x-2)(x+4)=x^3+2x^2-8x.

So if Q>0, the inequality holds

(1) means that x<-1.5

x and x-2 are negative, but x+4, and thus Q, could be either positive or negative
NOT SUFF


(2) x>-3. x+4 is positive, but x and x-2 and thus Q could be either positive or negative. NOT SUFF

(1) and (2) -3<x<-1.5

x and x-2 are negative and x+4 is positive. Thus Q>0. SUFF
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Does |x(x-2)(x+4)|= x^3+2x^2-8x ? (1) |x+2| < |x+1| (2) x 13 Sep 2006, 18:28
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I choose C.

1) means x < -1.5
2) means x > -3


both together will make that equation right.
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Does |x(x-2)(x+4)|= x^3+2x^2-8x ? (1) |x+2| < |x+1| (2) x 14 Sep 2006, 03:58
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kevincan
Does |x(x-2)(x+4)|= x^3+2x^2-8x ?

(1) |x+2| -3
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A.

1) |x+2| -3

x could be any number greater than -3. E.g. -2, 1. For 1, |x(x-2)(x+4)| Does not equal x^3+2x^2-8x...INSUFF



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