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All answers having "Hype" as clue:

4 Character Answers:

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BUZZ

PLUG

SELL

TALK

TOUT



5 Character Answers:

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BOOST

SHILL



6 Character Answers:

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HOOPLA



7 Character Answers:

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PROMOTE

PUFFERY



8 Character Answers:

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BALLYHOO

TALKITUP