Hi omyrichard, i find your question interesting and such phrases usually confuse me. I'vee looked up in the dictionary , and there's some difference between keep quite and be quite Be quiet means you refuse to talk or stop talking, fall silent Ex: The children shut up when their father approached. Keep quiet relates much to sensitive or confidential information that you should not reveal.
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Either one should be acceptable. I have often heard the same thing said either way.