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Hi,

You are right, as a student or even as a person under the age of 26 you get into most museums for free or for a discounted rate. If over 26 then you can buy a card for 4 museums for 40SEK. I am not sure how long you are going to be here for but it would probably be cheaper for you to buy a 3 day travel card for the public transport system (150 SEK) and go to museums etc as you like. I have found in the past with family and friends visiting that you only get value out of the gothenburg card if you cram A LOT into your day i.e. 3 museums or activities. Below is a link to the public transport system, it is in swedish but translates well in google translate (unfortunately if you click on english on the site the information provided is very limited).

See point 2 of link
http://www.vasttrafik.se/#!/biljetter-priser/turist---besokskort/tredygnsbiljett/

If you need any more info about Gothenburg please ask. I live here, love the place and am happy to share any knowledge I have with you :-)