(1) We prove that, provided n > 4, a permutably reducible n-ary quasigroup is uniquely specied by its values on the n-ples containing zero. (2) We observe that for each n, k > 2 and r 6 k/2 there exists a reducible n- ary quasigroup of order k with an n-ary subquasigroup of order r. As corollaries, we have the following: (3) For each k > 4 and n > 3 we can construct a permutably irreducible n-ary quasigroup of order k. (4) The number of n-ary quasigroups of order k > 3 has double-exponential growth as n → ∞; it is greater than exp exp(n ln k/3 ) if k > 6, and exp exp( ln 3 n− 3 0.44) if k = 5.