  The identifications of quasars in the redshift range 2.2<z<3 are known to be
very inefficient as their optical colors are indistinguishable from those of
stars. Recent studies have proposed to use optical variability or near-IR
colors to improve the identifications of the missing quasars in this redshift
range. Here we present a case study by combining both factors. We select a
sample of 70 quasar candidates from variables in SDSS Stripe 82, which are
non-UV excess sources and have UKIDSS near-IR public data. They are clearly
separated into two parts on the Y-K/g-z color-color diagram, and 59 of them
meet or lie close to a newly proposed Y-K/g-z selection criterion for z<4
quasars. 44 of these 59 sources have been previously identified as quasars in
SDSS DR7, and 35 among them are quasars at 2.2<z<3. We present spectroscopic
observations of 14 of 15 remaining quasar candidates using the Bok 2.3m
telescope and the MMT 6.5m telescope, and successfully identify all of them as
new quasars at z=2.36 to 2.88. We also apply this method to a sample of 643
variable quasar candidates with SDSS-UKIDSS nine-band photometric data selected
from 1875 new quasar candidates in SDSS Stripe 82 given by Butler & Bloom based
on the time-series selections, and find that 188 of them are probably new
quasars with photometric redshifts at 2.2<z<3. Our results indicate that the
combination of optical variability and optical/near-IR colors is probably the
most efficient way in finding 2.2<z<3 quasars and very helpful for constructing
a complete quasar sample. We discuss its implications to the ongoing and
upcoming large optical and near-IR sky surveys.
