is ×€x×€ less than I?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat May 14, 2011 1:27 am

If x is not equal to 0, is ×€x×€ less than I?

(1) x/×€x×€ < x.

(2) ×€x×€ > x.

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Source: Beat The GMAT — Data Sufficiency | Sat May 14, 2011 1:27 am

clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Sat May 14, 2011 4:21 am

got C here
(1) 1 st is valid for x=2, but it is not with in -1<x<1
or x=-1/2, and -1/2 is with in -1<x<1, insuff
(2) st 2 true for any x<0,also insuff
both give us -1<x<0 so suff

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pankajks2010: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 12:51 amFollowed by: 1 member; Location: New Delhi, India; Thanked: 12 times

by pankajks2010 » Sat May 14, 2011 7:13 am

statement 1: case a: x is positive, 1<x (satisfies)
case b: x is negative, -1<x (does not satisfies in the domain -1<x<0)
Thus, 1 alone is insufficient

Statement 2 can be reduced to x<0, Now, -1<x<0 satisfies the condition, however, x<-1 does not. Thus, it alone is insufficient.

Combining both, -1<x<0, which satisfies the condition. Thus, C

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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Sat May 14, 2011 10:34 am

Edit: NVM found -1 < x < 0 is valid for statement 1

Guys I'm getting (A)... what am I missing?

If x is not equal to 0, is |x| < 1?

(1) x/|x| < x

Multiplying by |x| on both sides won't change sign and we get x < x|x|
For this to be possibe x > 1, thus x = GT(1)
|GT(1)| < 1 ? Answer is no. Sufficient

(2) |x| > x
For this to be possible x < 0, thus x = LT(0)
|LT(0)| < 1 ? Can't answer with certainty. Insufficient

"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Sat May 14, 2011 10:56 am

MAAJ wrote:Edit: NVM found -1 < x < 0 is valid for statement 1

Guys I'm getting (A)... what am I missing?

If x is not equal to 0, is |x| < 1?

(1) x/|x| < x

Multiplying by |x| on both sides won't change sign and we get x < x|x|
For this to be possibe x > 1, thus x = GT(1)
|GT(1)| < 1 ? Answer is no. Sufficient

(2) |x| > x
For this to be possible x < 0, thus x = LT(0)
|LT(0)| < 1 ? Can't answer with certainty. Insufficient

hi MAAJ
in st 1 you missed that it is valid not only for x>1, but also -1<x<0, try to insert x=-1/2 in the st 1 and you`ll see that it satisfies both st 1 and problem as whole

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