Bunuel wrote:
Is (a − 5)^2 < (b + 5)^2 ?
(1) a < b
(2) a + b > 5
Simplifying the question stem:
\((a-5)^2-(b+5)^2<0\) or \((a-5+b+5)(a-5-b-5)<0\) or \((a+b)(a-b-10)<0\).
Hence the question becomes
IS \(a+b<0\) & \((a-b-10)>0\)
or \((a+b)>0\) & \((a-b-10)<0\)
Statement 1: \(a<b\) or \(a-b<0\) so we can say that \(a-b-10<0\) (as it is summation of two negative terms)
but we know nothing about \(a\) & \(b\) so whether \(a+b<0\) or \(a+b>0\) can't be arrived at. For example if \(a=-3\) & \(b=-1\), then \(a+b<0\) as well as \(a-b<0\) but if \(a=1, b=2\), then \(a+b>0\) but \(a-b<0\). Hence the statement is
not sufficient.
Statement 2: this implies that \(a+b>0\) but we know nothing about \((a-b)\), hence can't say that whether \(a-b-10<0\) or \(a-b-10>0\). For ex. if \(a=-1, b=7\) then \(a-b-10<0\) but if \(a=-1, b=13\) then \(a-b-10>0\). Hence
insufficientCombining 1 & 2
we know that \(a-b<0\), hence \(a-b-10<0\) and \(a+b>5\) hence \(a+b>0\). therefore \((a+b)(a-b-10)<0\). Hence sufficient
Option
C