A growing number of studies are using machine learning models to accurately predict antimicrobial resistance (AMR) phenotypes from bacterial sequence data. Although these studies are showing promise, the models are typically trained using features derived from comprehensive sets of AMR genes or whole genome sequences and may not be suitable for use when genomes are incomplete. In this study, we explore the possibility of predicting AMR phenotypes using incomplete genome sequence data. Models were built from small sets of randomly-selected core genes after removing the AMR genes. For Klebsiella pneumoniae, Mycobacterium tuberculosis, Salmonella enterica, and Staphylococcus aureus, we report that it is possible to classify susceptible and resistant phenotypes with average F1 scores ranging from 0.80-0.89 with as few as 100 conserved non-AMR genes, with very major error rates ranging from 0.11-0.23 and major error rates ranging from 0.10-0.20. Models built from core genes have predictive power in cases where the primary AMR mechanisms result from SNPs or horizontal gene transfer. By randomly sampling non-overlapping sets of core genes, we show that F1 scores and error rates are stable and have little variance between replicates. Although these small core gene models have lower accuracies and higher error rates than models built from the corresponding assembled genomes, the results suggest that sufficient variation exists in the core non-AMR genes of a species for predicting AMR phenotypes.