Hope you are doing well. Your question is unclear, can you specify what do you mean by minimum score in college predictor?
Nevertheless, I am sharing the general CAT percentile required for an individual to get into IIM A. Now, in order to get into IIM A, information regarding your Graduation, Gender (Male/Female), Reservation if any is also required. The group that faces the most difficulty here are GEM (General, Engineering, Male). For them, a safe percentile is 99.4 - 99.5. However, depending on these 3 attributes, you can also get admission in IIM A with only 98.2 percentile.
P.S. There are exceptional cases also, wherein candidates got in with very low percentiles, but these are very rare and you should not rely on them.
Hope this helps.