Inequality

[crackgmat007]

Can someone solve this pls?

OA - A

[raleigh]

(i) b - a > b-b(=0) > 1/(a-b)

So (i) is sufficient.

(ii) Choose a = 1/2, b = 0. Then 1/(a-b) = 2 and b-a = -1/2
Now choose a = 0, b = 1/2. Then 1/(a-b) = -2 and b-a = 1/2.

So (ii) is insufficient. Correct answer is A.

[crackgmat007]

(i) b - a > b-b(=0) > 1/(a-b)

So (i) is sufficient.
quote]

I am not clear with the above!! Can anyone explain in detail

[cramya]

Is 1/ a-b < b-a

Stmt I

a<b => a-b<0

1/a-b -> negative

We can write b-a as b - a = - (a - b)

If a-b is neagtive then - (negative) = positive

1/a-b < b-a

SUFF

Stmt II

1 < |a-b|

Even though |a-b| is positive , a-b can be positive or negative which makes b-a negative or positive so we can't tell if 1/a-b < b-a or not.

INSUFF

Hope this helps!

Regards,
CR

[crackgmat007]

tx much, very helpful

[lunarpower]

the first thing to notice in this problem is the presence of the expressions (a - b) and (b - a).
(a - b) and (b - a) are opposites. therefore, exactly one of them is positive, and the other is negative.

this is the sort of thing you should notice right away, and should "take away" from this problem and store in your head for future use.

given this fact, the only way for this inequality to work is if (a - b) is negative and (b - a) is positive.

therefore:
REPHRASED QUESTION:
is b - a > 0?

FURTHER REPHRASE:
is b > a ?


once you have this rephrase, the sufficiency of #1 is trivial.

to show that #2 is insufficient, note that |a - b| is a symmetric expression; i.e., it's the same as |b - a| (each of these is "the distance between a and b"). given that symmetry, there's no way that this expression could determine which of the two is greater.

thus (a)

[mike22629]

I have found that with data sufficiency there is generally a lot of information hidden in the question.

Like Ron said, all the question is really asking you is is a>b?

This is because one side has to be negative and the other has to be positivie.

Logically deducing information like this for data sufficiency questions will make your life a lot easier and help you to answer the questions way faster.

Just remember to find out exactly what the question is asking before you attempt to answer it.