Select a row where certain columns never failed certain condition

Question

Consider the following rows that is returned from a query:

name  number
foo     1
foo     9
foo     10
foo     11
bar     12
bar     13
dumb    14

How do I select the name where the number of such name is never under 10, and appear at least twice so this case, i wanted it to return

name
bar

What I have tried:

select name from my_table
where number >= 10 #<--Problem
group by name
having count(*) >=2 

This works partially because it was not able to filter out foo. The problem of this query is that it will be able to filter out foo 1 and foo 9 but foo 10 and foo 11 will be returned.

Answer 1

select name from my_table 
group by name 
having count(*) >=2 and min(number) >= 10