Let ABCD be the parallelogram having adjacent sides AB=10 and BC=8Attachment:
GRE parallelogram (3).png [ 78.58 KiB | Viewed 34 times ]
In triangle $
ABD,AO=OD$, so BO is a median, using Apollonius theorem in triangle ABD , we get $
AB2+BD2=2(BO2+AO2)$ i.e. $
2(BO2+AO2)=102+82=164⇒BO2+AO2=82$ which is sum of the squares of half of the diagonals of the parallelogram.
The expression $
BO2+AO2=82$ can be true for many different integer/non-integer values of BO and AO out of which one pair is $
(BO,AO)/(AO,BO)=(√75,√7)$
So, the diagonals of the parallelogram are $
2×√75=10√3&2×√7=2√7$ out of which $
10√3$ is greater than 8 but $
2√7$ is less than 8 .
Hence a unique comparison cannot be formed between column $
A&$ column $
B$ quantities, so the answer is (D).