Another inequality challange?

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

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

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?

Hi guys,

do you think this to be a difficult question, a so called "700 level" question?

thanks!

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.

So, my answer is E).