It depends on the game. For example in BF4 you want a very good quad core. Lots of games made in recent years can take advantage of more than 2 cores. Besides, with a quad you can have an antivirus or browser working in the background while the game still gets enough cores for itself.
GPU is the most important part for running games at ultra. Lower end CPUs will give you less performance when paired with a lower end chip aka. "bottleneck." Quad core i5 is an awesome proc with out fluff on it you don't need. If that is too expensive go for the 6 core fx6300 from AMD.