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gen.	beg a question (This, however, begs another question CBET)
idiom.	raise the question (Баян)
media.	generate a question (bigmaxus); trigger a question (bigmaxus)
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gen.	leave someone asking questions (bookworm); be controversial (Ремедиос_П); be rife with problems (Ivan Pisarev); be associated with problems (Ivan Pisarev); be accompanied by problems (Ivan Pisarev); be subject host of problems (Ivan Pisarev); face challenges (Ivan Pisarev); face problems (Ivan Pisarev); encounter problems (Ivan Pisarev); run into problems (Ivan Pisarev); be rife with issues (Ivan Pisarev); be associated with issues (Ivan Pisarev); be accompanied by issues (Ivan Pisarev); be subject host of issues (Ivan Pisarev); face some issues (Ivan Pisarev); face issues (Ivan Pisarev); encounter issues (Ivan Pisarev); run into issues (Ivan Pisarev); be rife with challenges (Ivan Pisarev); be associated with challenges (Ivan Pisarev); be accompanied by challenges (Ivan Pisarev); be subject host of challenges (Ivan Pisarev); face some challenges (Ivan Pisarev); encounter challenges (Ivan Pisarev); run into challenges (Ivan Pisarev)
Игорь Миг	raise a red flag; raise flags
inf.	cause concern (к, по поводу и т. п.: cause concern for the accuracy of the data 4uzhoj)
rhetor.	raise questions (New York Times Alex_Odeychuk)

вызывать вопрос: 31 phrases in 8 subjects

Diplomacy	3
General	19
Idiomatic	2
Logic	1
Makarov	2
Mass media	2
Quotes and aphorisms	1
Rhetoric	1