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inequalities

by fruti_yum » Mon Aug 03, 2009 12:23 pm
Is |x| < 1 ?

(1) |x + 1| = 2|x – 1|

(2) |x – 3| > 0


Some body hellllllpppppppppppppp... My exam is in less than a week and I can't solve this question.. I'm freaking out!!

Please dwell on the approach.. not just the answer!! appreciate it

OA is C
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Source: — Data Sufficiency |
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by ssmiles08 » Mon Aug 03, 2009 1:35 pm
1) |x + 1| = 2|x – 1|

x + 1 = 2(x-1)

x + 1 = 2x - 2

x = 3

x + 1 = -[2(x - 1)]

x + 1 = -2x + 2

3x = 1

x = 1/3

Insufficient as there are two solutions.

2) |x – 3| > 0

x - 3 > 0

x > 3

-(x -3) > 0

x < 3

Insufficient as the answer can be yes or no.

Together:

x cannot be = 3 according to the second statement, which leaves us with only 1 solution x = 1/3.

is |1/3| < 1? ---> YES.

Sufficient. (C)
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by mehravikas » Mon Aug 03, 2009 10:02 pm
Can I ask you, when considering negative values for x, why have you not done:

-(x + 1) = -[2(x - 1)]

-x - 1 = -2x + 2
x = 1
ssmiles08 wrote:1) |x + 1| = 2|x – 1|

x + 1 = 2(x-1)

x + 1 = 2x - 2

x = 3

x + 1 = -[2(x - 1)]

x + 1 = -2x + 2

3x = 1

x = 1/3

Insufficient as there are two solutions.

2) |x – 3| > 0

x - 3 > 0

x > 3

-(x -3) > 0

x < 3

Insufficient as the answer can be yes or no.

Together:

x cannot be = 3 according to the second statement, which leaves us with only 1 solution x = 1/3.

is |1/3| < 1? ---> YES.

Sufficient. (C)
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by ssmiles08 » Tue Aug 04, 2009 4:34 am
mehravikas wrote:Can I ask you, when considering negative values for x, why have you not done:

-(x + 1) = -[2(x - 1)]

-x - 1 = -2x + 2
x = 1
Making both sides negative will give you the same solution as the first one.

IMO you made a calculation error. -x + 2x = 2+ 1
x = 3

-hope that helps.
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by mehravikas » Tue Aug 04, 2009 12:05 pm
I guess that's not a choice, that's what we have to do.

When x > 0

x + 1 = 2x - 2

When x < 0

- (x + 1) = -2(x-2)


Please correct if I am wrong.
ssmiles08 wrote:
mehravikas wrote:Can I ask you, when considering negative values for x, why have you not done:

-(x + 1) = -[2(x - 1)]

-x - 1 = -2x + 2
x = 1
Making both sides negative will give you the same solution as the first one.

IMO you made a calculation error. -x + 2x = 2+ 1
x = 3

-hope that helps.
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