  Let $A, B$ be $n\times n$ positive semidefinite matrices. Bhatia and Kittaneh
asked whether it is true $$ \sqrt{\sigma_j(AB)}\le \frac{1}{2} \lambda_j(A+B),
\qquad j=1, \ldots, n$$ where $\sigma_j(\cdot)$, $\lambda_j(\cdot)$, are the
$j$-th largest singular value, eigenvalue, respectively. The question was
recently solved by Drury in the affirmative. This article revisits Drury's
solution. In particular, we simplify the proof for a key auxiliary result in
his solution.
