The average monthly apartment rent in the city has soared past $3,000 for the first time, and the scarcity of housing is driving home hunters out to suddenly pricey Brooklyn and Queens, new reports on the super-tight market show. In contrast, the average national apartment rent is $1,062, a little more than one-third the average city rent of $3,017 excluding Staten Island, according to Reis Inc., a real-estate research firm. Second-place San Francisco isn’t even close, at a mere $1,998.82 a month. Residents who feel priced out of Manhattan may soon be priced out of the five boroughs altogether. Median...