Is |a b| 0 (2) |b|

Question

Is |a − b| < |a − c| ?

(1) a > 0

(2) |b| < |c|

gmatophobia · Answer

The question can be translated to :   Is the distance between 'a' and 'b' is less than the distance between 'a' and 'c'   or    Is 'a' closer to 'b' on a number line that it is to 'c'

Statement 1

a > 0

We know that 'a' lies to the right of 0 in a number line, but there is no information on the position of 'b' or of 'c'. Hence this statement will not help us get the answer to the question, and we can eliminate option A and option D.

Statement 2

|b| < |c|

Alright, this statement tells that the distance between 0 and 'b' is less than the distance between 0 and 'c'. In other words 'b' is closer to 0 on the number line than 'c' is. However, we do not know the position of 'a'.

Let consider two cases

Case 1

------A-----B----0--------------C-------

In this case 'a' is closer to 'b' than it is to 'c'.

Case 2

----------B----0--------------C-----A-

In this case 'a' is closer to 'c' than it is to 'b'.

Hence we can eliminate option B.

Combining

Combining doesn't help either as we still don't know the position of 'a' with respect to 'b' and 'c'. All we know from Statement 1 is that 'a' lies to the right of 0 in the number line, but the relative position is still not known. To visualize this consider the following cases -

Case 1

-----------B----0-A------------C-------

In this case 'a' is closer to 'b' than it is to 'c'.

Case 2

---------B----0--------------C-----A-

In this case 'a' is closer to 'c' than it is to 'b'.

Hence E

khumoyuns · Answer

Each statement is clearly not sufficient on its own.

Choose smart numbers:

Option 1. a = 4, b = 3, c = 6 => RHS > LHS

Option 2. a = 4, b = - 3, c = 6 => LHS > RHS

So, answer is E

TheBipedalHorse · Answer

Is |a − b| < |a − c| ?
Interpretation - is b farther away from a than what c is from a. In other words, is the distance between b and a greater than the distance between c and a

(1) a > 0
Interpretation - a is to the right of centre (0,0)
 - still gives us no possible idea about location of b and c
 - b can be farther away from a than c, or the opposite also can be possible.

(2) |b| < |c|
interpretation - c is farther away from the centre (0,0) than b 
 - gives us no possible idea about the location of a
 - a can be closer to c than b, or the opposite is also possible

combine (1) and (2)
 - a is to the right of centre (0,0) and c is farther away from centre than b is

three possible scenarios:

Case 1
----- ------------ --------------- -----------------

Case 2
--------- ----------------------- ---------------- ------------------- -------------------------

Case 3
-------- --------------- ----------- ----------------- ---------------------------------------------

As you can see, many cases are possible,

Case 4
-------------- ----------------------- ------------------- ------------------ -------------------------

Case 5
--------------- ------------- ----------------- --------------------- -------------------------

Case 6
--------------- ----------- ------------ ---------- -------------------------

Therefore both statements together are also not sufficient

Is |a b| < |a c| ? (1) a > 0 (2) |b| < |c|

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