It is now a sad truth that dual core CPU's have finally reached their limit. I speak as someone who has pushed a Core 2 Duo above and beyond the sum of it's parts. We are now at that sad time where they simply can not be made to keep up.
Many games now are getting very CPU intensive, these open ended survival games or large environment games being primary examples. (such as Space Engineers, Subnautica & GTA V)
With a 64 bit OS (which you have) you should still be able to just about manage many games on the market but you can expect some poor performance in even the menu's of new games. You will find odd conflicting results as your computer will handle some games fine and not others despite the games seemingly being of the same levels of detail and or size, hair pulling may become a thing for you very soon I'm afraid.
If I may offer you some alternate advice that will require a little more cash but will serve you better in the long run. I do appreciate budget control is important to you and as someone who has to do this on a budget often; I hope this may help you.
Do two things, it would double your expenditure but it's worth waiting the extra month and doing it this way: Copy paste " CMZ8GX3M2A1600C9 " into google and buy 8GB of it. It will cost you around £40. The reason for this is that in my opinion s the best 1600MHZ budget performance Ram ever manufactured and it will work on your current machine! This will boost your computers memory up to 12GB which will make a significant difference. This ram although far from top spec; it can still be of use in a new machine you buy later in life.
I would also reconsider the graphics card choice. For the same price you could get an R7 250 which is around 50% stronger. However that said I'd chose neither. A pre-owned ATI 7850 series would be around the same price and although older, is much stronger.
For slightly more cash a HD 7870 (which is similar to a GTX 8800 or R9 270) is even better and would cope for another few years. The HD 7870 is also one of my favorite cards released in the past few years.
If you buy these two things then can carry you by the skin of your teeth for at least another year with most games, a HD 7850 or 7870 will run anything on the market now at high detail levels and with that extra RAM you could force some life out of your PC for a bit longer then add into to a new PC later. The only thing you can't do much about now mate is the fact games are starting to need quad cores to run with any stability. There are some work around options depending on the game but they are not always reliable.
I have drifted away from your original question by advising you however; to give you a direct answer to your question: Any game that does not state it requires a quad core can be run on your system at low graphics.
With some tweaking it will just about run quad core dependent games such as GTA V and Dragon Age Inquisition but I wouldn't recommend it; stability would be poor.
I hope this helps, I'm sorry it's so long.
-Kane
Facebook
Twitter
Instagram