DSE 2008 Question 1: Index numbers and time-series basics

In the context of ideal price index numbers, consider: S1: the index should be invariant to the choice of base, i.e. $P_{rs}\cdot P_{sr}=1$. S2: an index that satisfies the circularity condition $P_{rs}\cdot P_{st}=P_{rt}$ (all $r,s,t$) need not satisfy S1. S3: if all prices change in the same proportion $\lambda$, the index should equal $\lambda$. S4: changing the units of measurement of the prices, but not those of the quantity weights, should not affect the index. Which of the following is true?