Absolute Value

[keizer Soze]

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

[kanha81]

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]

[keizer Soze]

Thanx Kanha, it seems that plug in mumbers is the best choice