A price-weighted index was created 2 months ago, using stocks A and B, then priced at $25 and $37, respectively. A month ago, A was trading at $19 and B was at $42, when it was decided that stock A would be replaced by stock C, then priced at $61. Stock C is currently trading at $57, stock A is priced at $31 and stock B is trading at $44. If no other changes were made to the index over the past month, the current value of the index equals ______.

Explanation: First note that a price weighted index is derived by summing up the prices of the constituent stocks and then dividing the sum by a divisor. When the index is first constructed with N stocks, the divisor equals N. Later on, when changes like stock splits or index composition take place, the divisor is adjusted so as to keep the value of the index constant across the change. In this case, just before stock A is replaced by C, the value of the index equals (19+42)/2 = 30.5. To prevent a change in the value of the index when stock C replaces A, the divisor must be changed from 2 to (61+42)/30.5 = 3.377. Thus, the current index value equals (57+44)/3.377 = 29.91