Will a gigabyte 2 gb gddr5 work with Intel i3-3220 (3.30ghz) or will it cause bottleneck

Solution
A GT 710 is good for use as a replacement for integrated graphics in general computer use. So if your computer has no integrated graphics, or it has poor integrated graphics, the 710 is one of your options. In this kind of use there will be no bottleneck.

If you plan to play games, this is not a good card to buy. Look for a GT 730 DDR5 if you must buy something very inexpensive and low end. Even then, you'll need to run games at 720p and some games won't run well even at 720p.

Your i3 3220 could use something better, like a GTX 1050, but I'm guessing that's out of your price range.
A GT 710 is good for use as a replacement for integrated graphics in general computer use. So if your computer has no integrated graphics, or it has poor integrated graphics, the 710 is one of your options. In this kind of use there will be no bottleneck.

If you plan to play games, this is not a good card to buy. Look for a GT 730 DDR5 if you must buy something very inexpensive and low end. Even then, you'll need to run games at 720p and some games won't run well even at 720p.

Your i3 3220 could use something better, like a GTX 1050, but I'm guessing that's out of your price range.
 
Solution