Delete rows based on duplicate names in 1 column if they contain a value in a second ?

I need to know if it is possible to delete all rows with duplicate names in column A if Column B contains a value for any of those rows with that same name?

Example Below: I need to be able to delete ALL rows below that have the name "APPLE" in Column A if any of those rows contains a "1" in Column B. So in this case, ALL 4 rows with "APPLE" need to be deleted even though the first row with "APPLE" doesn't contain a "1" in Column B. The same goes for name "DOG".

Column A Column B

BOOK
BOOK
APPLE
APPLE 1
APPLE 1
APPLE 1
CAT
CAT
CAT
CAT
DOG 1
DOG