Regulators found China’s fast-cooling property sector is in a dilemma and looking for a way out, said China observers, as cash-strapped builders default on their debt and sales plunge. As the peak season for home sales faded, sales fell in both new and resale homes overturning everything that Chinese people know as “Golden September and Silver October”—the two months that traditionally have upbeat property sales. By the end of October, the volume of second-hand housing transactions (36,000 units) in 13 principal cities in China had fallen back to where it was seven years ago, down over 40 percent from last year, Shanghai E-House Real Estate Research Institute found. Beijing saw its monthly turnover of second-hand properties slump for the seventh consecutive month to 9,340 units in October—the first time in the year that it fell below 10,000 units—flagging a 53.4 percent fall on a year-on-year basis. Prices of new homes …