The statement that must be true regarding a business designated as a 501(c)(3) is:
The business has federal tax exemptions.
501(c)(3) organizations are recognized as tax-exempt by the federal government, which means they do not have to pay federal income tax on the money they earn related to their exempt purposes.
The other statements are not necessarily true. A 501(c)(3) can earn profits, but those profits must be reinvested in the organization to further its charitable purposes. Additionally, a 501(c)(3) may be a private foundation or a public charity, but being one or the other is not guaranteed just by being classified as a 501(c)(3).