I was given a bike that cost £150. How can I tell if this bike is rubbish or not?
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Depends on your definition of rubbish! If I were to guess it is probably all entry level components, unless they have been upgraded. That would be the first indicator. You can cross reference them by typing model numbers into Google.
However, before throwing it away I would recommend putting it up for sale, or even better if there is someone in need, why not dust it off, polish it up and donate it to the less fortunate!
Now, little details was given on your post so it'd difficult to give accurate answer. Your bike is probably good for short commutes, but not for serious exercising. Also cheap bike usually is less attractive to thieves.
Cheap bikes also usually have weak parts and if you break something you can quickly go beyond economical repair.