We present a simultaneous single-dish survey of 22 GHz water maser and 44 GHz and 95 GHz class I methanol masers toward 77 6.7 GHz class II methanol maser sources, which were selected from the Arecibo methanol maser Galactic plane survey (AMGPS) catalog.Water maser emission is detected in 39 (51%) sources, of which 15 are new detections. Methanol maser emission at 44 GHz and 95 GHz is found in 25 (32%) and 19 (25%) sources, of which 21 and 13 sources are newly detected, respectively. We find 4 high-velocity (> 30 km/s) water maser sources, including 3 dominant blue- or redshifted outflows.The 95 GHz masers always appear with the 44 GHz maser emission. They are strongly correlated with 44 GHz masers in velocity, flux density, and luminosity, while they are not correlated with either water or 6.7 GHz class II methanol masers. The average peak flux density ratio of 95 GHz to 44 GHz masers is close to unity, which is two times higher than previous estimates. The flux densities of class I methanol masers are more closely correlated with the associated BGPS core mass than those of water or class II methanol masers. Using the large velocity gradient (LVG) model and assuming unsaturated class I methanol maser emission, we derive the fractional abundance of methanol to be in a range of 4.2*10^-8 to 2.3*10^-6, with a median value of 3.3pm2.7*10^-7.
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