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Related to keen: dictionary
treat them mean, keep them keen
Neglecting a romantic partner (or a potential romantic partner) keeps him or her interested in you. A: "Why hasn't Tom called me yet? I thought he liked me." B: "Maybe he thinks that 'treat them mean, keep them keen' actually works."
be as keen as mustard
To be very enthusiastic about something. Primarily heard in UK, Australia. These new kids are as keen as mustard to be in the choir, so we can definitely get them to clean up the choir room for us.
be keen about
To be excited about or interested in something. Rich is very keen about this cruise he's planned for the fall. Don't take this opportunity if you aren't keen about it.
See also: keen
be keen on
To be excited about or interested in someone or something. I'm glad that Jimmy and Lena are finally going on a date, since he's been keen on her for months. Don't take this opportunity if you aren't keen on it.
have a keen interest in something
to have a strong interest in something; to be very interested in something. Tom had always had a keen interest in music, so he started a band. The children have a keen interest in having apet, so I bought them a cat.
keen on doing something
willing or eager to do something. Dave isn't very keen on going to the opera. The children are keen on swimming this afternoon. Shall I take them?
keen on someone or somethingand keen about someone or something
to be enthusiastic about someone or something. I'm not too keen on going to Denver. Sally is fairly keen about getting a new job. Mary isn't keen on her new boss.
be as keen as mustard(British & Australian old-fashioned)
to be very eager Why don't we ask Tom to captain the cricket team? He's as keen as mustard.
keen about, be
Be enthusiastic about. For example, He's been keen about this whole endeavor for a long time. It is also put as be keen on, which has the additional meaning "to be ardent about or in love with," as in Jim's been keen on Jane for years. With other adverbs, such as keen at and keen of, keen has been so used since the early 1500s; the current locutions, however, date from the mid-1800s.
See also: keen
mod. fine; excellent. Your idea is really peachy!