I believe that particular figure originally comes from http://www.nyc.gov/html/om/pdf/2010/pr267_10_report.pdf http://www.nyc.gov/html/om/pdf/2010/pr267_10_repo

I believe that particular figure originally comes from http://www.nyc.gov/html/om/pdf/2010/pr267_10_report.pdf http://www.nyc.gov/html/om/pdf/2010/pr267_10_report.pdf and https://graphics8.nytimes.com/packages/pdf/national/20070307HomelessYouth.pdf https://graphics8.nytimes.com/packages/pdf/national/20070307... . 40% is at the upper end of the estimates, and any specific figure should obviously be taken with a pinch of salt, given the difficulties inherent in obtaining precise data of this nature. However, there is little doubt that LGBT people are substantially overrepresented in homeless populations. This is the case in many cities and countries, not just NYC.