Will this work?

[UtterTulip]

Will a R7240 work on a off brand 300w psu?

[lani100]

Will a R7240 work on a off brand 300w psu?

Yes. 

[UtterTulip]

Thanks

[Electronics Wizardy]

I don't suggest you buy a r7 240 as they are not much faster than onboard and if you want to game you get a huge improvement going to a 100 dollar gpu 

[mgsstar]

Will a R7240 work on a off brand 300w psu?

A system that has a R7 240 in a 2550K overclocked loads at around 120W so you will be able to run it on a 300W. What are your specs of your system and what do you plan to do with this system/gpu?