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shinewine
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Is |x|< 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 26 Aug 2006, 09:21
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Qc5:
Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3|≠ 0



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Is |x|< 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 26 Aug 2006, 10:22
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C for me..

To prove |x| <1
=> is -1<x<1 ?

From 1:

(x-3)(3x-1)=0
=>x=3 OR x=1/3 INSUFF

From 2:

|x-3| !=0

=> x-3 !=0 OR -x+3 !=0
=>x !=3 OR -x!=-3
=> x!=3
INSUFF

From 1 and 2,
x=1/3

Hence C
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GMATT73
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Is |x|< 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 26 Aug 2006, 10:31
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Futuristic
C for me..

To prove |x| <1
=> is -1<x<1 ?

From 1:

(x-3)(3x-1)=0
=>x=3 OR x=1/3 INSUFF

From 2:

|x-3| !=0

=> x-3 !=0 OR -x+3 !=0
=>x !=3 OR -x!=-3
=> x!=3
INSUFF

From 1 and 2,
x=1/3

Hence C
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Used identical method. So ! also means not equal too? hmmm
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Futuristic
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Is |x|< 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 26 Aug 2006, 11:18
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GMATT73
Futuristic
C for me..

To prove |x| <1
=> is -1<x<1 ?

From 1:

(x-3)(3x-1)=0
=>x=3 OR x=1/3 INSUFF

From 2:

|x-3| !=0

=> x-3 !=0 OR -x+3 !=0
=>x !=3 OR -x!=-3
=> x!=3
INSUFF

From 1 and 2,
x=1/3

Hence C

Used identical method. So ! also means not equal too? hmmm
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!= means not equal to in the C programming language
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gk3.14
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Is |x|< 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 Updated on: 26 Aug 2006, 18:32
Originally posted by gk3.14 on 26 Aug 2006, 16:59.
Last edited by gk3.14 on 26 Aug 2006, 18:32, edited 1 time in total.
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Futuristic..
Can you explain how you got:

from |x+1| = 2|x-1|

to (x-3)(3x-1)=0


I usually substitute + and -ve values to the equation;

So I get x+1 = 2x -2 ; x= 3 for both positive
-x -1 = -2x + 2; x x=3 for both negative
x + 1 = -2x +3 x = 1/3 for positive /negative

INSUFF

2. x-3 != 0; INSUFF

Combined x = -3 SUFF..

Am I missing something obvious/
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trivikram
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Is |x|< 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 26 Aug 2006, 17:04
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gk3.14
Futuristic..
Can you explain how you got:

from |x+1| = 2|x-1|

to (x-3)(3x-1)=0


I usually substitute + and -ve values to the equation;

So I get x+1 = 2x -2 ; x= 3
-x + 1 = -2x -2; x = -3
INSUFF

2. x-3 != 0; INSUFF

Combined x = -3 SUFF..

Am I missing something obvious/
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square both side you would get it
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Futuristic
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Is |x|< 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 26 Aug 2006, 22:35
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[quote="gk3.14"]Futuristic..
Can you explain how you got:

from |x+1| = 2|x-1|

to (x-3)(3x-1)=0


I usually substitute + and -ve values to the equation;

So I get x+1 = 2x -2 ; x= 3 for both positive
-x -1 = -2x + 2; x x=3 for both negative
x + 1 = -2x +3 x = 1/3 for positive /negative

INSUFF

2. x-3 != 0; INSUFF

Combined x = -3 SUFF..

Am I missing something obvious/[/quote


I used to follow the method you mentioned above. The easier way is to square both sides, which removes the 'absoluteness', and then solve.
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heman
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Is |x|< 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 26 Aug 2006, 23:47
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[quote="shinewine"]Qc5:
Is |x| is -1 Qstem is No
x=1/3--> Qstem is Yes
BCE
(2) |x - 3|≠ 0
x=4 Qstem = No
x=1/2 Qstem = Yes
CE
(1)&(2)
x=1/3 Qstem = Yes

Hence C

Heman



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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