can an intel i3 3220 run a GTX 760?

Solution
The Core i3-3220 will work with the GTX 760. However, as mentioned above in games that use more than 2 cores the i3-3220 will bottleneck the GTX 760.

For example, BioShock Infinite is a pretty easy game on just about any modern system. It only uses 2 cores and as long as the CPU is fast enough the GPU will not be bottlenecked. See below CPU performance chart with a GTX 680 which is more powerful than the GTX 760. Performance is pretty close for AMD and Intel CPU regardless if they have 2 cores or 8 cores.

Skyrim is an example of CPU intensive game, but it only uses 2 cores. Therefore, in general the GTX 760 will give you better performance with an Intel CPU than an AMD CPU.

Hitman: Absolution represents one of the more demanding...

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@ 720p possibly...though for similar/less money you could get the FX 6300 which would not bottleneck the 760.
 
The Core i3-3220 will work with the GTX 760. However, as mentioned above in games that use more than 2 cores the i3-3220 will bottleneck the GTX 760.

For example, BioShock Infinite is a pretty easy game on just about any modern system. It only uses 2 cores and as long as the CPU is fast enough the GPU will not be bottlenecked. See below CPU performance chart with a GTX 680 which is more powerful than the GTX 760. Performance is pretty close for AMD and Intel CPU regardless if they have 2 cores or 8 cores.

Skyrim is an example of CPU intensive game, but it only uses 2 cores. Therefore, in general the GTX 760 will give you better performance with an Intel CPU than an AMD CPU.

Hitman: Absolution represents one of the more demanding games out there. Most games released are not as demanding as Hitman many game publishers tries to appeal to as many people as possible including those who do not have high end systems so that they can sell as many copies of the game as possible. This games does benefit from a quad core CPU. If you look at the performance chart below, the performance difference between the i3-3220 @ 3.3GHz and the i5-3470 @ 3.2GHz is 12FPs; a difference of 26%. However, 46FPS is still playable with the Radeon HD 7970.

Now we go to Crysis 3. Crysis 3 is the exception, not the rule. The vast majority of games are not as demanding as Crysis 3. Crysis 2 was a cakewalk because Crytek wanted it to run well on consoles and sell as many games a possible. Crysis 3 brings us back to the era of the original Crysis where even the best hardware at the time only give you decent performance. The Core i3-3220 more or less chokes on this game as can be seen in the performance chart below. You will still be able to play the game though if you turn down the graphics settings, but performance will still be lower compared to a quad core CPU.


http://www.techspot.com/review/655-bioshock-infinite-performance/page5.html

CPU_03.png


http://www.techspot.com/review/608-hitman-absolution-performance-benchmarks/page6.html

CPU_01.png


http://www.techspot.com/review/642-crysis-3-performance/page6.html

CPU_03.png
 
Solution
Since you will be playing at 720p resolution you should get good FPS with the GTX 760 and Crysis 3 should be playable on the i3-3220. Especially since 720p is less than half the resolution of 1200p.

Between the Core i3-3220 and the FX-6300... In games that do not really care how fast the CPU is as long as it does not bottleneck the GPU (like BioShock) the performance should basically be the same. In CPU intensive games that only use 2 cores (like Skyrim), the i3-3220 will give you better performance even if the FX-6300 was overclocked. In CPU dependent games that uses 4 cores the FX-6300 will perform better than the i3-3220.

If you had the money, the answer would be to simply buy a quad core i5 CPU. However, since you are working with a relatively small budget the choice seems to be between the i3-3220 and the FX-6300. The vast majority of games only use 2 cores so on average you don't really need a quad core CPU. However, the specific games you want to play may be able to take advantage of 4 cores.

As stated, Crysis 3 is an exception, not the rule. Most CPU demanding games will be more like Hitman: Absolution (such as Metro 2033 / Last Light) were a dual core CPU will still good frame rates, but not as high as a quad core CPU can. However, if you look at the performance chart again you should note that while this game can make use of 4 cores, the dual core i3-3220 still outperforms the 6 core FX-6300, but only by 3 FPS.