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# If x ? 0, is x^2/|x| < 1? (1) x < 1 (2) x >

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Intern
Joined: 08 May 2006
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If x ? 0, is x^2/|x| < 1? (1) x < 1 (2) x > [#permalink]

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15 Aug 2006, 21:13
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If x ≠ 0, is x^2/|x| < 1?

(1) x < 1
(2) x > −1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Manager
Joined: 25 Jul 2006
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15 Aug 2006, 21:21
C

If x ≠ 0, is x^2/|x| < 1?

(1) x < 1
(2) x > −1

If x> 0 then X*X/ X <1
If x< 0 then X*X / -X ( - because mod of a negative number is that number into -1) = X*X/-X <1 => -X< 1=> X> -1

thus C

This is definitely a tricky question; my first inclination would be to mark A.

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Intern
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15 Aug 2006, 21:28
Dont you think.

since for x<0 |x| will be -x

so x^2 /|x| for x < 0 .. will be x^2 /-x= -x

which will be less than 1

x^2/|x| < 1

so from A we can make out the answer

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Manager
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15 Aug 2006, 21:38
Check your ans for x = -2, x = -1/2 & x = 1/2 !

Achilless wrote:
Dont you think.

since for x<0 |x| will be -x

so x^2 /|x| for x < 0 .. will be x^2 /-x= -x

which will be less than 1

x^2/|x| < 1

so from A we can make out the answer

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Manager
Joined: 12 May 2006
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16 Aug 2006, 00:29
C...

The only way that this equation could be less than 1 is if it were between -1 & 1

(eg decimal)

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Senior Manager
Joined: 14 Jul 2005
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16 Aug 2006, 00:47
C it is ... the equation holds true when -1<x<1

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CEO
Joined: 20 Nov 2005
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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16 Aug 2006, 00:59
We don't have to worry about the -ve values. The equality will behave same for +ve and -ve values. We just need to worry about the fractions less than 1 and greater than 0 because x^2 is less than x for |x|<1.

So this is a straight C.
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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16 Aug 2006, 00:59
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