Wonderful Question

statement 1: Sufficient

since a is negative

choosing a =-2 ad b=-3 plugging in will give consistent no
-----------a= -2 and b=-4 plugging will give same

hence sufficient

statement 2: insufficient

choose a=0 and b= 1 yields no as answer

now searching for a number to get a yes and hopefully knock this out for sufficiency

a=2 and b =1 yields a no and a yes hence insufficient..

imo qa is A

I think D

Stm 2 we cannot chose 0 for a as per the question. and stm 2 implies that either b =0 or both a and b are negative...plug in a=2, b=0 or a=-1 b=-1 suff

If a and b are integers, and |a| > |b|, is a · |b| < a – b?
(1) a < 0
(2) ab is equal or greater than 0

Definetly E

Main stem a · |b| < a – b, or b < a – a · |b|, or b < a ( 1- |b|)
So, the Q is:
Is b < a ( 1- |b|)?

(1)
Nothing about b, so INSUFF just to check:
a<0. I hate to pick numbers, but
2 options:
b>0.
a=-5, b=1 then b > a ( 1- |b|)?

a<0, b<0
a=-5, b=-2 then -2 < -5 * ( -1 ) or b < a ( 1- |b|)

INSUFF


(2)
ab is equal or greater than 0
4 options:
a>0 with b>0
a<0 with b<0. a=-5, b=-2 then -2 < -5 * ( -1 ) or b < a ( 1- |b|)
a>0 with b=0
a<0 with b=0. a=-5, b=0 then 0 > -5 * ( 1 ) or b > a ( 1- |b|)
INSUFF


(1)(2)
a<0 with b<0. a=-5, b=-2 then -2 < -5 * ( -1 ) or b < a ( 1- |b|)
a<0 with b=0. a=-5, b=0 then 0 > -5 * ( 1 ) or b > a ( 1- |b|)
INSUFF

E

4meonly wrote:If a and b are integers, and |a| > |b|, is a · |b| < a – b?
(1) a < 0
(2) ab is equal or greater than 0

Definetly E

Main stem a · |b| < a – b, or b < a – a · |b|, or b < a ( 1- |b|)
So, the Q is:
Is b < a ( 1- |b|)?

(1)
Nothing about b, so INSUFF just to check:
a<0. I hate to pick numbers, but
2 options:
b>0.
a=-5, b=1 then b > a ( 1- |b|)?

a<0, b<0
a=-5, b=-2 then -2 < -5 * ( -1 ) or b < a ( 1- |b|)

INSUFF


(2)
ab is equal or greater than 0
4 options:
a>0 with b>0
a<0 with b<0. a=-5, b=-2 then -2 < -5 * ( -1 ) or b < a ( 1- |b|)
a>0 with b=0
a<0 with b=0. a=-5, b=0 then 0 > -5 * ( 1 ) or b > a ( 1- |b|)
INSUFF


(1)(2)
a<0 with b<0. a=-5, b=-2 then -2 < -5 * ( -1 ) or b < a ( 1- |b|)
a<0 with b=0. a=-5, b=0 then 0 > -5 * ( 1 ) or b > a ( 1- |b|)
INSUFF

E

4meonly, good work!

This is a MGMAT question and I am not sure whether it really represents an authentic GMAT question but there are so many take aways we can all benefit from this question.