* Robust construction lifts property amid gloomy Nov econ data. : BEIJING (Reuters) - Property investment in China picked up in November, in contrast to other key data where growth weakened sharply, though soft home sales and land purchases pointed to a dim outlook for the sector amid a slowing broader economy. Real estate investment, which mainly focuses on the residential sector but includes commercial and office space, rose 9.3 percent in November from a year earlier, accelerating from 7.7 percent in October, according to Reuters calculations based on data released by National Bureau of Statistics (NBS) on Friday.