My answer is different from the correct answer - Please help

[ggmat007]

Is 1 / (a-b) < (b-a)? (1) a < b (2) 1 < |a-b|

Answer: A

Approach:

Rephrase: Is 1<(a-b)(b-a)?

1) a < b
If a, b are both +ve, Both -ve, or -ve & +ve
1 > (a-b) (b-a)
Statement (1) is sufficient.

2) 1 < |a-b|

case 1: a-b>1 if a-b>0 or a>b
case 2: b-a>1 if a-b<0 or a<b

For case 2 we know that the statement 1 > (a-b) (b-a) is always true

Even for case 1: a>b, (a,b) = (9,7) or (-7,-10) or (7,-2) we get: 1 > (a-b) (b-a) is always true

and therefore statement 2 is also sufficient.

My answer is D but the correct answer is A. Can anyone please help me understand why statement 2 is not sufficient and where is the problem with my approach.

Thanks in advance

[GMATGuruNY]

Is 1 / (a-b) < (b-a)?

(1) a < b
(2) 1 < |a-b|

Rephrase: Is 1<(a-b)(b-a)?

When you multiplied each side of the inequality in the question stem by a-b, you presumed that a-b>0.
If a-b<0, then the direction of the inequality symbol in your rephrase must FLIP from < to >.
Since the sign of a-b is unknown, it's safer not to rephrase the question stem.

Statement 1: a < b
Thus:
a-b < 0.
b-a > 0.
Here, we can rephrase 1/(a-b) < b-a as follows:
1/(negative) < positive.
negative < positive.
SUFFICIENT.

Statement 2: 1 < |a-b|
Case 1: a-b = 2, implying that b-a = -2.
If we plug a-b = 2 and b-a = -2 into 1/(a-b) < b-a, we get:
1/2 < -2
NO.

Case 2: a-b = -2, implying that b-a = 2.
If we plug a-b = -2 and b-a = 2 into 1/(a-b) < b-a, we get:
1/(-2) < 2
-1/2 < 2.
YES.

Since in the first case the answer is NO, but in the second case the answer is YES, INSUFFICIENT.

The correct answer is A.

[bubbliiiiiiii]

Statement 2: |a-b| < 1.

I think this should be reverse?

[GMATGuruNY]

Statement 2: |a-b| < 1.

I think this should be reverse?

Yes -- edited my reply above.