  We present results of a study of 12 dust-reddened quasars with 0.4 < z < 2.65
and reddenings in the range 0.15 < E(B-V) < 1.7. We obtained ACIS-S X-ray
spectra of these quasars, estimated the column densities towards them, and
hence obtained the gas:dust ratios in the material obscuring the quasar. We
detect all but one of the red quasars in the X-rays. Even though there is no
obvious correlation between the X-ray determined column densities of our
sources and their optical color or reddening, all of the sources show absorbed
X-ray spectra. When we correct the luminosity for absorption, they can be
placed among luminous quasars; therefore our objects belong to the group of
high luminosity analogues of the sources contributing to the X-ray background
seen in deep X-ray observations. Such sources are also found in serendipitous
shallow X-ray surveys. There is a hint that the mean spectral slope of the red
quasar is higher than that of normal, unobscured quasars, which could be an
indication for higher accretion rates and/or an evolutionary effect. We
investigate the number density of these sources compared to type 2 AGN based on
the X-ray background and estimate how many moderate luminosity red quasars may
be found in deep X-ray fields.
