keizer Soze wrote:I need to find a shortcut for this one (I searched it but I couldn´t find it):
If a and b are integers, and |a| > |b|, is a · |b| < a – b?
(1) a < 0
(2) ab >= 0
OA E
wow! what a prob it indeed is! I went as methodically as I could
(i) a=-2 < 0 => |a| = |-2| = 2
case-1: b=1>0
|2| > |1|: -2*1 < -2-1 => -2 < -3. No
case-2: b=-1<0
|2| > |1|: -2*|-1| < -2+1 => -2 < -1. Yes
Insuff
(ii) ab>=0
case-1: a=2>0, b=1>0
2*1 < 2-1 => 2 < 1. No
case=2: a<0, b<0
-2*|-1| < -2+1 => -2 < -1. Yes
case-3: (a>0 or a<0), b=0
-2*|0| < -2-0 => 0 < -2. No
2*|0| < 2-0 => 0 < 2. Yes
Insuff
(i) & (ii)
a<0 & ab>=0 we've covered all the possiblities. we don't get
all Yes's or
all No's
Insuff. hence [spoiler][E][/spoiler]
Want to Beat GMAT.
Always do what you're afraid to do. Whoooop GMAT
