CAT (DILR) PYQs

There are four bottles. Each bottle is known to contain only P or only I. They will be considered to be “collectively ready for despatch” if all of them contain only P. In minimum how many tests, is it possible to ascertain whether these four bottles are “collectively ready for despatch”?.

What is the number of $500$ rupee notes required to serve $50$ customers with $500$ rupee notes as their preferences and another $50$ customers with $100$ rupee notes as their preferences, if the total number of notes to be dispensed is the smallest possible?

If the ATM could serve only $10$ customers with a stock of fifty $500$ rupee notes and a sufficient number of notes of other denominations, what is the maximum number of customers among these $10$ who could have given $500$ rupee notes as their preferences?