Pupils at the primary education level are less violent and are hard workers.
Do we need "are" and what is the natural thing to do?
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As the sentence stands, you need the second are in there for 2 reasons.
Having two are's in close proximity might seem a little clumsy though. (could just be me).
To fix this I would suggest a more natural sounding way to say this would be to switch them around:
Pupils at the primary education level are harder working and less violent.
Either is acceptable, but if you repeat the verb, it will be less confusing.
With the repeated verb, it is clear that you mean to say that the pupils [are less violent (in general)] and [are hard workers].
Without the repeated verb, it could also be (mis)understood that you mean to say that the pupils are [less violent workers] and [hard workers], or even that the pupils are [less violent workers] and [less hard (diligent) workers].