x / |x| < x

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clawhammer: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Aug 15, 2010 10:08 am; Thanked: 3 times; Followed by:1 members

x / |x| < x

by clawhammer » Tue Nov 30, 2010 4:45 am

Please assist with my understanding:

if, x / |x| < x, then how should I rephrase the equation when x is negative?

(A) x / -x > x
or, (B) x / -x < x

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Source: Beat The GMAT — Problem Solving | Tue Nov 30, 2010 4:45 am

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pm; Location: Milpitas, CA; Thanked: 447 times; Followed by:88 members

by Rahul@gurome » Tue Nov 30, 2010 6:27 am

clawhammer wrote:Please assist with my understanding:

if, x / |x| < x, then how should I rephrase the equation when x is negative?

(A) x / -x > x
or, (B) x / -x < x

Choice B, i.e. x/|x| < x => x/(-x) < x
Because here you're just putting the value of |x|.
Only when both side of an inequality is multiplied with a negative number, the inequality sign reverses.

In this particular question this confusion shouldn't arise at all because x/|x| is equal to 1 for positive x and -1 for negative x. Just replace x/|x| with 1 or -1 for positive or negative analysis.

Rahul Lakhani
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