Something Wrong with the question???

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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 am; Location: Ahmedabad; Thanked: 31 times; Followed by:10 members

Something Wrong with the question???

by ronnie1985 » Wed May 23, 2012 10:51 am

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

The question is 1<(b-a)(a-b)
Now (b-a)*(a-b) = -1(a-b)*(a-b) = -(a-b)^2

hence the question asks if 1 < a negative number which is absurd.

The OA is [spoiler](A)[/spoiler]

Follow your passion, Success as perceived by others shall follow you

Quote

Source: Beat The GMAT — Data Sufficiency | Wed May 23, 2012 10:51 am

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Wed May 23, 2012 1:03 pm

ronnie1985 wrote:Is 1/(a-b)<(b-a)?
1. a<b
2. 1<|a-b|

The question is 1<(b-a)(a-b)
Now (b-a)*(a-b) = -1(a-b)*(a-b) = -(a-b)^2

hence the question asks if 1 < a negative number which is absurd.

The OA is [spoiler](A)[/spoiler]

Hi!

Remember - when inequalities and variables are involved, you have to be very careful with your manipulations!

You cannot simply cross-multiply by a-b, since it's possible that a-b is negative. If a-b IS negative, then when you cross multiply you get:

Is 1/(a-b)<(b-a)?
Is 1 > (b-a)(a-b)?
Is 1 > -1(a-b)(a-b)?
Is 1 > -(a-b)^2?

So, if a-b is positive, you get a "NO" answer to the question; if a-b is negative you get a "YES" answer to the question.

Since (1) tells us that a-b<0, it's sufficient to answer the question. (2) doesn't tell us anything about the sign of (a-b), so it's insufficient. Choose (A)!

* * *

As an aside, if you ever wonder whether a question is valid, make sure you include the source! (Even better, always include the source.)