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anshulseth: Master | Next Rank: 500 Posts; Posts: 145; Joined: Mon Feb 16, 2009 8:41 amFollowed by: 2 members; Thanked: 2 times

by anshulseth » Mon May 04, 2009 5:11 am

If x≠0, is |x| <1?
(1) x2<1
(2) |x| < 1/x

OA: D

Please explain the working.

Last edited by anshulseth on Mon May 04, 2009 7:51 am, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Mon May 04, 2009 5:11 am

btg760: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Sun May 03, 2009 7:12 am; Thanked: 6 times

by btg760 » Mon May 04, 2009 6:22 am

Can you please complete the question? Second statement is incomplete.

For 1st statement, proceed like this:-

Question asked is |x| < 1, that means, x should lies between -1 and 1

Since x^2 < 1 therefore, x will be always in the range -1 to 1. Hence statement (1) is sufficient.

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anshulseth: Master | Next Rank: 500 Posts; Posts: 145; Joined: Mon Feb 16, 2009 8:41 amFollowed by: 2 members; Thanked: 2 times

by anshulseth » Mon May 04, 2009 7:51 am

My bad. Have edited it.

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iriijei.idwimd: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Jan 27, 2009 9:37 am

by iriijei.idwimd » Mon May 04, 2009 10:50 am

I think the 1st option is already explained in prev post.

lets take 2nd option

given |x| < 1/x , need to determine |x| <1

|x| < 1/x is never true for any -ve numbers.
|-100| < -1/100 ==> 100 < -1/100 (false)

try positive numbers ( 0 to 1, > 1)
for x>1 , say 5 == 5 < 1/5 false.
try 0 to 1, this holds true

when x belongs to (0,1) we can say |x| < 1.

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Mon May 04, 2009 11:11 am

|x| < 1/x

revers:
1/|x| >x
1>x|x|

if x<0, 1>-x^2 or x^2>-1 alwas true
x>0=> 1>x^2 x^2<1 so |x|<1

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dumb.doofus: Master | Next Rank: 500 Posts; Posts: 435; Joined: Sat Sep 27, 2008 2:02 pmFollowed by: 1 member; Location: San Jose, CA; Thanked: 43 times; GMAT Score:720

by dumb.doofus » Mon May 04, 2009 12:14 pm

maihuna wrote:|x| < 1/x

revers:
1/|x| >x
1>x|x|

if x<0, 1>-x^2 or x^2>-1 alwas true
x>0=> 1>x^2 x^2<1 so |x|<1

You cannot multiply like what you have done in the part that I have highlighted above.. in inequalities, sign does matter. and without knowing the sign of x, you cannot multiply coz the inequality may change.

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