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
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Another inequality challange?
Source: Beat The GMAT — Data Sufficiency |
Given-|a|>|b|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?
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?
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
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Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Location: Vancouver, BC
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The missing part is your conclusion that a and b must be positive.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?
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
Hi guys,
do you think this to be a difficult question, a so called "700 level" question?
thanks!
do you think this to be a difficult question, a so called "700 level" question?
thanks!
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GMAT/MBA Expert
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Brent@GMATPrepNow
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I'd classify this question somewhere in the 600-700 range.
My $0.02
My $0.02
Brent Hanneson - Creator of GMATPrepNow.com
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).
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).
