UPSC 2015 CDS I Math Paper

=3√a×b×c=3
⇒a×b×c=27
⇒3√d×e×f
⇒d×e×f=64
The least arithmetic mean M is obtained when a = b = c = 3 and d = e = f = 4.
Therefore, the least value of M
Also, M ≠ 3.5 as at least three elements among a, b, c, d, e, f are distinct, which will give the value of M greater than M (one such set is a = 3, b = 3, c = 3, d = 2, e = 4, f = 8).
∴M>3.5