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why is it enough?

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why is it enough?

by finance » Fri Jul 22, 2011 7:35 am
I m having difficulties in understanding why the
statement b^2>a^2 is enough to answer the data
sufficiency question (a-b)/(b+a)<1??

I understand that |b|>|a|, but Im still confused.
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by pemdas » Fri Jul 22, 2011 9:15 am
first of all b^2>a^2 can be translated into not only |b|>|a| but also into b^2-a^2>0 and further into (b-a)(b+a)>0 which breaks down to

.... (b-a)>0 and (b+a)>0 OR
.... (b-a)<0 and (b+a)<0

note (b-a)>0 is also true for (a-b)<0. Given we have two options with the exact inequalities described above (after four dots :) ), we get (a-b)<0 and (b+a)>0 OR (a-b)>0 and (b+a)<0. In both options we get the negative sign for the ratio (a-b)/(b+a) which means Sufficient and we answer Yes (a-b)/(b+a)<1 as (a-b)/(b+a)<0

finance wrote:I m having difficulties in understanding why the
statement b^2>a^2 is enough to answer the data
sufficiency question (a-b)/(b+a)<1??

I understand that |b|>|a|, but Im still confused.
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by goalevan » Fri Jul 22, 2011 4:22 pm
b^2 > a^2
b^2 - a^2 > 0
(b + a)(b - a) > 0
(a + b)(b - a) > 0
-(a + b)(a - b) > 0
(a + b)(a - b) < 0

If and only if xy < 0, x and y have opposite signs. Similarly, if and only if x/y < 0, x and y have opposite signs.

Since (a + b)(a - b) < 0, we know that a + b and a - b have opposite signs, therefore (a + b)/(a - b) < 0 < 1.
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