  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.
