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

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Senior Manager
Joined: 10 Mar 2008
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If x ≠ 0, is x^2/|x|< 1? (1) x < 1 (2) x > −1 [#permalink]

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13 Oct 2008, 21:30
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If x ≠ 0, is x^2/|x|< 1?
(1) x < 1
(2) x > −1

Could some please explain as to how to simply the question. Thanks!
SVP
Joined: 29 Aug 2007
Posts: 2476
Followers: 70

Kudos [?]: 774 [0], given: 19

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13 Oct 2008, 21:54
vksunder wrote:
If x ≠ 0, is x^2/|x|< 1?
(1) x < 1
(2) x > −1

Could some please explain as to how to simply the question. Thanks!

"x^2 / |x| < 1?" can be re-arranged as "x^2 < |x| ?"

then from
1: if x < 1, x could be +ve fraction, -ve fraction or -ve integer/number.. nsf.
2: if x > -1, x could be a -ve fraction, +ve fraction or +ve integer/number.. nsf.

from 1 and 2: -1 < x < 1. so x is either a +ve or -ve fraction. in that case, lxl is always > x^2.

so it is C.
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SVP
Joined: 17 Jun 2008
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13 Oct 2008, 22:09
vksunder wrote:
If x ≠ 0, is x^2/|x|< 1?
(1) x < 1
(2) x > −1

Could some please explain as to how to simply the question. Thanks!

x^2 can be written as |x| * |x| and hence x^2/|x| can reduce to |x|.

|x| will be smaller than 1 only when -1<x<1 and hence C should be the answer.
SVP
Joined: 05 Jul 2006
Posts: 1747
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14 Oct 2008, 13:07
1
KUDOS
vksunder wrote:
If x ≠ 0, is x^2/|x|< 1?
(1) x < 1
(2) x > −1

Could some please explain as to how to simply the question. Thanks!

REWRITE

X^4 / X^2 <1

X^2<1

ie: is /x/< 1

obviously C
Senior Manager
Joined: 10 Mar 2008
Posts: 361
Followers: 5

Kudos [?]: 290 [0], given: 0

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14 Oct 2008, 15:26
Thanks for the explanation guys! OA - C.
Re: DS   [#permalink] 14 Oct 2008, 15:26
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