Mongolian men have no qualms about asking for directions when they're not sure of the way,1 which is lucky because I could count on one hand the number of road signs I spotted — and the road signs follow the same rules as maps in Mongolia.
Namely, they're just supposed to be, you know, vaguely approximate.
Even leaving aside the whole left/right dilemma,2 I'd swear to you that monastery was far more than 35km beyond the sign.