When querying Knowledge Bases (KBs), users are faced with large sets of data, often without knowing their underlying structures. It follows that users may make mistakes when formulating their queries, therefore receiving an unhelpful response. In this paper, we address the plethoric answers problem, the situation where a query produces significantly more results than the user was expecting. We deal with this problem by identifying the parts of the failing query, called Minimal Failure Inducing Subqueries (MFIS), that cause plethoric answers. As long as the query contains an MFIS, it will fail to reach a sufficiently low amount of answers. Thanks to these MFIS, interactive and automatic approaches can be set up to help the user reformulate their query. The dual notion of MFIS, maXimal Succeeding Subqueries (XSS), is also useful. They are queries with the most parts of the original query that return non plethoric answers. Our goal is to compute MFIS and XSS efficiently, so that they may be used to solve the plethoric answers problem. We propose two algorithms that leverage query and data properties to compute MFIS and XSS. We show experimentally that our algorithms clearly outperform a baseline method on generated queries as well as real user-submitted queries.