We present measurements of partial branching fractions of $B \rightarrow K^+ X$, $B \rightarrow K^0 X$, and $B \rightarrow \pi^+ X$, where $X$ denotes any accessible final state above the endpoint for B decays to charmed mesons, specifically for momenta of the candidate hadron greater than 2.34 (2.36) GeV for kaons (pions) in the B rest frame. These measurements are sensitive to potential new-physics particles which could enter the $b \rightarrow s(d)$ loop transitions. The analysis is performed on a data sample consisting of $383 \times 10^6$ $B \bar{B}$ pairs collected with the BaBar detector at the PEP-II $e^+e^-$ asymmetric energy collider. Our results are in agreement with standard model predictions and exclude large enhancements of the inclusive branching fraction due to sources of new physics. Show Partial Abstract