inequality

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inequality

by arorag » Sun Aug 03, 2008 6:45 pm
is 1/a-b < b-a ???

1. a<b
2.1> abs a-b

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by parallel_chase » Mon Aug 04, 2008 12:10 am
I think there is something wrong with the second statement. While posting a question kindly check if you have posted the question correctly or not.

Statement I is sufficient.

Therefore the answer will be either A or D depending on the second statement.

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by Vignesh.4384 » Mon Aug 04, 2008 1:32 am
Hi parallel_chase,

About option A.

I simplified the question as follows

Question 1/(b-a) < (a-b)

1 < (b-a) (a-b)

1 > (b-a) (b-a)

1 > (b-a)^2

Is this correct ?

If this is correect then we cant conclude from option A right ?

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by parallel_chase » Mon Aug 04, 2008 1:50 am
Vignesh.4384 wrote:Hi parallel_chase,

About option A.

I simplified the question as follows

Question 1/(b-a) < (a-b)

1 < (b-a) (a-b)

1 > (b-a) (b-a)

1 > (b-a)^2

Is this correct ?

If this is correect then we cant conclude from option A right ?

I think everything is correct except for the last step.

-1 > (b-a)^2.

If you do this the statement I is sufficient because for any value of a or b it will always be greater than -1, the answer would be no and statement will be sufficient.

Let me know what you think.

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by Vignesh.4384 » Mon Aug 04, 2008 2:10 am
I make stupid silly mistakes al the time ..
Thanks parallel_chase. i got it

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by parallel_chase » Mon Aug 04, 2008 3:18 am
Vignesh.4384 wrote:I make stupid silly mistakes al the time ..
Thanks parallel_chase. i got it
Dont thank me yet.

If you notice you cannot simplify the equation, because you dont know the values of a or b weather they are positive or negative, therefore you cannot simplify the equation because you are dividing and multiplying the variables.

If you could do that, this can never be a data sufficiency question.

Hence you have to take the original inequality as is.

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Re: inequality

by Ian Stewart » Mon Aug 04, 2008 6:40 am
arorag wrote:is 1/a-b < b-a ???

1. a<b
2.1> abs a-b
I think the above solutions are overcomplicating matters. From 1:

a < b, so b - a > 0 and a - b < 0.

If a-b is negative, so is 1/(a-b). So of course it's less than b-a, which is positive. Sufficient.

From 2 (which I've understood to say 1 > |a-b|), a-b could be positive or negative. Insufficient. A.

That said, if you did want to do this algebraically, from 1) you know that a-b<0. So if you multiply both sides of the inequality by (a-b), you need to reverse the inequality:

1/(a-b) < (b-a)
1 > (b-a)(a-b)

Then multiplying by -1, we again need to reverse the inequality:

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

which must be true; (a-b)^2 can't be less than zero.
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