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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Another inequality challange? ##### This topic has expert replies Junior | Next Rank: 30 Posts Posts: 21 Joined: 28 Sep 2008 ### Another inequality challange? by callmemo » Sun Nov 02, 2008 8:05 pm If a and b are integers, and |a| > |b|, is a * |b| < a – b? (1) a < 0 (2) ab >= 0 OA: E Anyone for an easy explination? Last edited by callmemo on Sun Nov 02, 2008 9:09 pm, edited 1 time in total. Legendary Member Posts: 2467 Joined: 28 Aug 2008 Thanked: 331 times Followed by:11 members by cramya » Sun Nov 02, 2008 9:00 pm Can u please chekc these 2 things in the question |a| > |b|, is a · |b| < a – b? Is it a * |b| Also Stnt 2 is its ab > 0 Master | Next Rank: 500 Posts Posts: 496 Joined: 04 May 2008 Location: mumbai Thanked: 7 times GMAT Score:640 ### Re: Another inequality challange? by stubbornp » Sun Nov 02, 2008 9:01 pm callmemo wrote:If a and b are integers, and |a| > |b|, is a · |b| < a – b? (1) a < 0 (2) ab 0 OA: E Anyone for an easy explination? Given-|a|>|b| four possiblities-a=-3,b=-2 a=-3,b=2 a=3,b=-2 a=3,b=2 stmt 1:a<0 two possiblities left a=3,b=-2 a=3,b=2 stmt 2:ab=0 it means a.|b|=0 0<a-b? we ve four possiblits for a and b---so insufficent Combine 1 and 2,two possibilies again Again we are unable to conclude the signs for a and b-- Answer should be E...hope it helps Junior | Next Rank: 30 Posts Posts: 21 Joined: 28 Sep 2008 by callmemo » Sun Jan 18, 2009 6:26 am I. Not Sufficient a < 0 => b can be either positive or negative eg. a = -3, b = -2 or + 2 if b = -2; a * |b| < a – b => true if b = 2; a * |b| < a – b => false II. Sufficient ab >= 0 => Given |a| > |b|; a or b can't be zero. so a,b must be positive. a=1, b = 2; a * |b| < a – b => false a=3, b = 2; a * |b| < a – b => false But OA is E. What am I missing? ### GMAT/MBA Expert GMAT Instructor Posts: 14908 Joined: 08 Dec 2008 Location: Vancouver, BC Thanked: 5254 times Followed by:1263 members GMAT Score:770 by Brent@GMATPrepNow » Sun Jan 18, 2009 6:54 am ab >= 0 => Given |a| > |b|; a or b can't be zero. so a,b must be positive. a=1, b = 2; a * |b| < a – b => false a=3, b = 2; a * |b| < a – b => false But OA is E. What am I missing? The missing part is your conclusion that a and b must be positive. We could have a= -3 and b=-2 (as you suggested earlier in your solution) Also, your first set of numbers to plug in (a=1 and b=2) breaks the condition that |a| > |b| Brent Hanneson - Creator of GMATPrepNow.com If you enjoy my solutions, I think you'll like my GMAT prep course Watch these video reviews of my course And check out these free resources Master | Next Rank: 500 Posts Posts: 353 Joined: 20 Jan 2007 Location: Italy Thanked: 7 times GMAT Score:720 by mjjking » Sun Jan 18, 2009 8:35 am Hi guys, do you think this to be a difficult question, a so called "700 level" question? thanks! Beat The GMAT - 1st priority Enter a top MBA program - 2nd priority Loving my wife: MOST IMPORTANT OF ALL! REAL THING 1 (AUG 2007): 680 (Q43, V40) REAL THING 2 (APR 2009): 720 (Q47, V41) ### GMAT/MBA Expert GMAT Instructor Posts: 14908 Joined: 08 Dec 2008 Location: Vancouver, BC Thanked: 5254 times Followed by:1263 members GMAT Score:770 by Brent@GMATPrepNow » Sun Jan 18, 2009 8:50 am I'd classify this question somewhere in the 600-700 range. My$0.02
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by vishu » Mon Jan 19, 2009 2:02 pm
Here's my take on this q:

If a and b are integers, and |a| > |b|, is a * |b| < a – b?

(1) a < 0

a =-6, b = 2
-12 < -8 ? yes
a = -3, b = 0
0 < -3? no
Hence, (1) is INSUFFICIENT.

(2) ab >= 0

There can be two cases that satisfy this condition.
Case 1: a <=0 and b <= 0
Case 2: a >=0 and b >= 0

Take case 1: a <=0 and b<=0
a=-3,b=-1
-3 < -2 ? Yes
a = -5, b = 0
0 < -5 ? No

No need to go any further. Hence, (2) is INSUFFICIENT as well.

(3) Taking both (1) and (2) together, we find that a < 0 and b <=0. From case 1 in 2) we know that this is INSUFFICIENT.