It's hard to say Macedon really conquered the Persians; most of the people actually running the territory -Persian satraps- remained in charge, and Alexander didn't have enough troops to really garrison the empire and enforce his will everywhere. What he did was defeat a succession of Persian armies in pitched battles; while the Persian Empire was several times larger than Macedon, logistical limitations meant that they couldn't field armies of corresponding relative size. While possessing 30,000 troops against 50,000 puts one at a disadvantage, it's not insurmountable, and Alexander was of course a gifted war leader whose father had assembled a disciplined and powerful army. After tearing down the Achaemenid dynasty, though, the new territory swallowed him; conquering the world on horseback is easy, but dismounting and ruling is hard.