Is 3x the rent based on total household income?

Usually, yes. Most landlords add together the gross income of every adult who signs the lease and compare the total to 3 times the rent. Two roommates earning $2,400 a month each have $4,800 between them, which passes on a $1,500 apartment even though neither would qualify alone.

Only people on the lease count. A partner who lives there without signing adds nothing to the application, however much they earn.

Some landlords do it differently and require each roommate to meet the standard alone, or to earn 3 times their own share of the rent. Student housing often works this way. The listing wording tells you which: "combined household income" means incomes are added. See household income for what is included.