I heard a different version of this one.

Once G. K. was riding alone in the mountains and stumbled upon a some kind of holy man. G. K. felt for him for some reason and told him his biggest problem: he had many sons and grandsons, but didn't have a clue whom to appoint as his heir. The holy man advised him to ask them a number of questions, including the one about the greatest pleasure. So G.K. did. Some of his sons and grandsons said the pleasure was in wine, and others in falcon hunting, birth of your first son, etc. etc. etc. G.K. began to wonder if the holy man was so wise after all, when the last one he asked, the youngest grandson called Batu, said this phrase about lamentation of women. "Fine", said Genghis Khan, "You'll be in charge when I die".

This is just a legend, but Batu did hear lots of lamentation...