Assume that you construct a price weighted index of 30 stocks. The sum of the prices of these stocks is $2000. The divisor for this index is 30, and the value of this index is 100. Now assume that one of the 30 stocks, with an average price of $100, has a three-for-one stock split while the value of other stocks remains unchanged.

a) If you make no adjustments to the index, what will be the new value of the index?

b) What does the new divisor have to be to keep the value of the index unchanged at 100?