median is 130,000 let price of rest of 14 homes is X.
(130,000 + 14X)/15 = 150,000
(130,000 + 14X) = 2,250,000
14X=1,12,0000
X=80,000
So avg price of rest of the 14 homes is 80,000.
with the assumption that the three choices are given excluding the median priced home the choice would be III only.
What is the OA?
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If we consider first 8 home-prices (sorted list) 130k, then we have a
solution for which
8*130k + 7*x = 15 * 150k
x ~ 172k
Since the above condition can exist, we can discard II and III.
To validate I, consider the least price for the max-priced home.
This can happen if all homes are the average (150k) but we know
that median is 130k.
So, least value for max-priced home = 130k * 8 + x*7 i.e. the last
7 homes are of same value. Even this condition shows x ~ 172k and
so there should be atleast 1 home priced > 165k.
Hence A
solution for which
8*130k + 7*x = 15 * 150k
x ~ 172k
Since the above condition can exist, we can discard II and III.
To validate I, consider the least price for the max-priced home.
This can happen if all homes are the average (150k) but we know
that median is 130k.
So, least value for max-priced home = 130k * 8 + x*7 i.e. the last
7 homes are of same value. Even this condition shows x ~ 172k and
so there should be atleast 1 home priced > 165k.
Hence A
