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Since 15 homes, the 8th home price in ascending order is 130K
If we choose first 7 homes also to be 130K, which is a possibility we can eliminate III (Ans: C & E)
Additionally, if we choose last homes to 170K (in order to get an average) we can eliminate II (Ans: B & D)
We are left with I. We can simply choose or if we see the median price as 130, which is 20K less than mean price. So atleast one home should be mean + price diff (20K) = 170K (Hence I is true -> Ans: A).
total homes = 15
average price = 150k
total price = 2,250,000
median (8th highest house) sold for 130k
I) if median is 130k, then the max. total for the first 8 houses are 130k*8 = 1,040,000
total price - 1,040,000 = 1,210,000 for the total remaining highest 7 houses which yield a value close to 170k so this is TRUE
II) first part of the statement has to be true since (I) is true, but 2nd part isn't b/c of the same explanation in (I) so FALSE
III) going back to (I) we see that it is still possible to have the first 8 houses at 130k and still be able to achieve an avg. price of 150k so this is FALSE