New York landlords: tenant income screening criteria?

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I just bought my first rental house in the Bronx and am currently renovating it.  Once the renovations are done, I would like to rent it out ASAP.  I came across very useful articles on this site, include this one about the four pillars of tenant screening: http://www.biggerpockets.com/renewsblog/2014/05/12...

It recommends requiring that tenants make gross income of at least 3.5X the rent.  That doesn't seem too feasible in New York, where rents are very high overall.  To all you New York landlords, what income criteria do you use? 

I was checking demographic information on realtor.com, clrsearch.com, and city-data.com.  The average rent in the Bronx neighborhood of my rental house is $1474, while median household income is 27,590, or $2299.17/month, only 1.56 times average monthly rent.  And in the Manhattan neighborhood where I live, average rent is $2521, median household income $38,035 or $3169.58/month, or 1.26 times average monthly rent.  I would think it would be hard to find tenants in New York who satisfy the gross income of 3.5x rent requirement.