Unless the apartment is rent controlled or rent stabilized the landlord is free to raise the rent to whatever he thinks the market will bear. Maybe your mom should look for a new apartment and/or seek a longer term lease to prevent these large unexpected increases.
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If your mother's apartment is rent stabilized, the landlord may only raise the rent as provided in the lease renewal offer in the amounts allowed by the New York City Rent Guidelines Board.
If your mother's tenancy is not regulated by the Rent Stabilization Law, New York State takes no position on the amount a landlord may seek for a new or increased rent if the landlord offers a renewal lease, That is left to the tenant and the landlord to negotiate in the free and unregulated market.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.