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With a AR score of 20 and a CAT percentile of 98.6 in the year 2016 the person did not get a call from the old IIM'S. So I think this shoish give you a picture.
Also one very important point is that CAT is based off percentile. Meaning your rank is based in relation to the people you wrote with in that year. It is relative. So a specific number cannot be given as cat score.
One major plus point is your humanities background. IIM'S are pushing big time for diversity and with a good profile, you stand a great chance!
All the best!
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