Is |a| |b|? (1) 1/(a − b) 1/(b − a) (2) a + b

Question

Is |a| > |b|?

(1) 1/(a − b) > 1/(b − a)

(2) a + b < 0

MaryKaaviya · Answer

Answer is C 1) 1/(a-b)>1/(b-a) ==> 2/(a-b)>0 a-b>0 insuff 2) a+b<0 insuff Combining ==> case 1: a,b <0 |a|<|b| case 2: b<0 |a|<|b| sufficient (C)

santosh93 · Answer

Given statement 1:
  \frac{1}{a-b}>\frac{1}{b-a}

can't we re-arrange the above equation as 
(b-a)>(a-b)
2b>2a
b>a
As b>a, which can be used to answer the problem statement i.e. |a| > |b|

TestPrepUnlimited · Answer

Hi  santosh93  ,

This is a common mistake. This exact expression is a bit special but in general, when you see variables in inequalities we have to be cautious. Here what you did was "multiply both sides by (a - b) then (b - a)" but we don't know if these two terms are positive or negative. We wouldn't know if the inequality should result in ">" or "<", thus we wouldn't be allowed to "move" these terms without knowing the signs.

However, we do know (a - b) and (b - a) have OPPOSITE signs so no matter what the result is  b - a < a - b  for this expression and we get  b < a  (this is still insufficient alone).

Hope that helps!

TestPrepUnlimited · Answer

Statement 1:

Normally we are not allowed to move variables around in an inequality using multiplication/division but  a - b  and  b - a  have opposite signs so no matter what this simplifies to  b - a < a - b  and  b < a . This is still insufficient as we can have  -5 < 3  vs  -1 < 3 .

Statement 2:

(a, b) = (3, -5) vs (a, b) = (-3, -1). Insufficient.

Combined:

We may write statement 2 as  a < -b . Combining  b < a  from statement 1 we have  b < a < -b  which means b must be negative. Since  a  is between both b's,  a 's magnitude must be less than that of b, which we can translate to  |a| < |b| . Sufficient.

Ans: C

imaityaroy · Answer

My 2 cents:
a != b because if they are equal then the inequality will become infinite (1 divided by 0 = infinite) which is not a valid solution in gmat

If a and b are not same then a-b and b-a will have opposite signs (try #'s if you doubt this statement)

S(1) -> Given 1/(a-b)> 1/(b-a) we know LHS will be positive and RHS will be negative ...but this does not ensure |a|>|b|... all we can take away from this statement is that a is greater than b
so 2 cases -> a = 1 and b = -10 .....then |a|<|b|.
a = 10 and and b = -1 ...then |a|>|b|.
hence insufficient

S(2) -> a+b<0 .... a <-b
so 2 cases -> a = -1 and -b = 10 .....then |a|<|b|.
a = -10 and -b = 1...then |a|>|b|.

combining statement 1 and 2

b<a<-b

a is between b and a on the numberline hence |a|<|b|

thus c is sufficient

Is |a| > |b|? (1) 1/(a − b) > 1/(b − a) (2) a + b < 0

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions