A Q-algebra (ξ; *, 0) is a generalization of the concepts of BCK, BCI-algebras, introduced by Neggers et al. [1]. As for BCK, BCI-algebras, the concept ideal is defined for Q-algebras [1]. In this paper, we show that for a given integer n, and for all k ∈ {0, 1, …, log2n – 1}, there is a Q-algebra ξ of cardinality n such that the G-part G(ξ) = {υ ∈ ξ :  0 * υ = υ} is an ideal of ξ with |G(ξ)|= 2k. Moreover, we show that if G(ξ) is an ideal of a Q-algebra ξ and |ξ|= n, then |G(ξ)|= 2k, for some k ∈ {0, 1, 2, …, log2 n – 1}.