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bmwhype2
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20.33 abs val 19 Nov 2007, 11:16
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Is |x+1| < 2?

1. (x-1)^2 < 1
2. x^2 - 2 < 0

please explain your answers.



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Ravshonbek
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20.33 abs val Updated on: 19 Nov 2007, 13:35
Originally posted by Ravshonbek on 19 Nov 2007, 13:12.
Last edited by Ravshonbek on 19 Nov 2007, 13:35, edited 3 times in total.
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bmwhype2
Is |x+1| < 2?

1. (x-1)^2 < 1
2. x^2 - 2 < 0

please explain your answers.
Show more


1.
x-1<1
x<2
and
-(x-1)<1
1-x<1
x>0

so

0<x<2. not suff. x=1.5 or x=1/2 not suff.

2.
x^2 - 2 < 0
x^2<2
x<sqrt2
or
x>-sqrt2

so

-sqrt2<x<sqrt2 not suff. ex. x=1.3 no. or x=-1.3 yes

combined:

-sqrt2<x<0 and 0<x<sqrt2 not suff.

E.


any other inputs
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Ravshonbek
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20.33 abs val 19 Nov 2007, 13:18
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sorry i have to edit my answer. illl shortly post it
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KillerSquirrel
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20.33 abs val 19 Nov 2007, 13:30
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Is |x+1| < 2 ?

-x-1 < 2
x > -3

or

x < 1

statement 1

(x-1)^2 < 1

x = 1 ---> true
x = 0 ---> true

insufficient

statement 2

x^2 - 2 < 0

x = 1 ---> true
x = 0 ---> true

insufficient

both statements

x^2 -2x < 0

x^2 - 2 < 0

-2x+2 < 0

2x < 0

x < 0

insufficient

the answer is (E)

:)
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bkk145
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20.33 abs val 19 Nov 2007, 13:39
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bmwhype2
Is |x+1| < 2?

1. (x-1)^2 < 1
2. x^2 - 2 < 0

please explain your answers.
Show more


E

The question is asking if -3<x<1

(1) 0<x<2
INSUFFICIENT

(2) -1.4<x<1.4
INSUFFICIENT

Together, 0<x<1.4 INSUFFICIENT
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walker
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Concentration: Entrepreneurship, Other
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Schools: Chicago (Booth) - Class of 2011
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20.33 abs val 19 Nov 2007, 13:53
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:-D
I'd like use drawing for inequality. Often it is faster end more resistant to errors.
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KillerSquirrel
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20.33 abs val 19 Nov 2007, 13:55
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walker
:-D
I'd like use drawing for inequality. Often it is faster end more resistant to errors.
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Nice !

:)



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