
The pair, aged 16 and 17, were detained by police following a threat made to Nova Training in Oldbury on January 28.
Both have since been bailed while investigations continue.
There have been a series of hoaxes in the West Midlands in recent weeks that have led to school closures.
Inspector Gareth Guest said: ‘These kinds of offences are not only a drain on police, council and school resources but they also waste the time of pupils who should be receiving their education.
‘We take reports like this very seriously.’
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