Is |a| > |b|?

(1) b < -a

(2) a < 0


Absolute inequalities have been really confusing me. After going through the book I was pretty confident that I would be able to tackle such questions easily. However, doing the QUESTION bank has really shaken my confidence. I only got 11 out of 25 right. I did them in timed conditions.

I was hoping if anyone will be kind enough to explain the best approach for tackling the question above? I am struggling to follow the explanation outlined in the Q Bank Solution. Thanks!!

my general approach to abs value problems is to start with "theory" and than plug in numbers to test solutions. if someone thinks of a more efficient method, please share

start with (2). it doesn't tell us anything about B and we have no way of comparing a to b so eluminate BD- > ACE only

try (1). b < -a. okay test numbers to try and figure out whether this is sufficient. it may be helpful to use a small table to organize your test cases

if a = -1 and b = -10000, then -a = 1 > 1000
if a = -1000 and b = 1, then -a = 1000 > 1

it is unclear whether abs (a) > abs (b) since we can make 2 cases where equation given in (1) holds

use both:
we know based on (2) that a<0 is negative so b <-a means that b is less than some positive number a. again test numbers.

if a = -1000, then -a= 1000 and b = 1, then 1 < 1000 and abs a > abs b

if a = -1, then -a = 1 and b = -1000, then -1000 < 1 and abs a < abs b

there are multiple cases that fit this so we can't answer with certainity whether abs a > abs b.

E

Thank you George--well done!

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Jamie Nelson
ManhattanGMAT Instructor