Yes I'll enlist down some of the top institutes for MBA whose cutoffs are between 80 to 90 percentile.

1. Tapmi Institute Manipal, CAT cutoff was 80 percentile.
2. KJ Somaiya Institute of Management And research, Mumbai,, 85 was the cutoff percentile -
3. IIM DELHI - cutoff percentile for cat exam was 90
4. BIMM Pune - cutoff 80
5. IIM Ghaziabad - cutoff 90

Thank-you. Best wishes.