Problem 24 of Hanna Neumann's book [3] reads: Does there exist, for a given integer n > 0, a Cross variety that is generated by its k-generator groups and contains (k+n)-generator critical groups? In such a variety, is every critical group that needs more than k generators a factor of a k-generator critical group, or at least of the free group of rank k? In a recent paper [1], R. G. Burns pointed out that the answer to the first question is an easy affirmative, and asked instead the question which presumably was intended: Given two positive integers k, l, does there exist a variety 23 generated by k-generator groups and also by a set S of critical groups such that S contains a group G minimally generated by k+l elements and S/{G} does not generate B? The purpose of this note is to record a simple example which shows that the answer to the question of Burns is affirmative at least for k = 2, l = 1, and also that the answer to the second question of Hanna Neumann's Problem 24 is negative.