Infinity Column - A Rara Avis

There again in the Wonderland of Alice's, there was a party the Mad Hatter arranged for his friends and foes alike. But despite that fact a vile foe of him poisoned a single tumbler of flavored serbet before he was caught red handed.But unfortunately in the hustle that followed, the poisoner himself forgot which tumbler he had poisoned.



When the Mad Hatter was informed of this fact and asked if the contents of all the tumblers had to be poured out in the sink, he came over and had a glance at the tumblers, then he smiled blissfully and asked to take a single tumbler out of them and  chemically test it for the poison. 

When the Mock Turtle asked if that would be enough, the Mad Hatter replied "Certainly not but that will strategically minimize our effort" .

At last the poisoned tumbler had been singled out after a few tests and the party went on forever afterward as ever repeating itself.

You have to find:

What was the exact number of tumblers? 

If  you  ask  me for a clue,  all I know,  as I  was  told by the Time himself, is  that  there were somewhere  between two hundred and three hundred tumblers of serbet to be served at the party.

Also, any group of tumblers can be tested simultaneously by taking a small aliquot of serbet from each, mixing the aliquots and making a single test of the mixture.