I got A.

I don't know how to explain this, I just thought conceptually.

If the Median is 130,000, that means atleast half are are at or below 130,000.

SO to have an average of 150,000 at least one house must be > 165,000

THe same doesnot hold true for II, and III.

If half houses are sold for under 130,000 and half are sold for > 150,000, that eliminates II.

III also does not have to be true. to have a median of 130, they can sell more than half for 130,000 and still have a median of 130,000.

this one took a lot of time for me to solve, still got it wrong...

on the test i ll guess on such a question n move on......

anyways thanks for the explanation !

7 houses under 130.000 and 7 houses above

I: It could be that all of the below-median houses are 129.999 and that could mean that above-median houses are all below 165.000

II: It could be that all below-median houses are 1, therefore al below median houses have to be > 150.000 to get the mean provided

III: A median of a odd number N implies that there are (N-1)/2 under the median --> (15-1)/2= 7 so there are 7 numbers below 130.000.


C

hazpazfaz wrote:7 houses under 130.000 and 7 houses above

I: It could be that all of the below-median houses are 129.999 and that could mean that above-median houses are all below 165.000

II: It could be that all below-median houses are 1, therefore al below median houses have to be > 150.000 to get the mean provided

III: A median of a odd number N implies that there are (N-1)/2 under the median --> (15-1)/2= 7 so there are 7 numbers below 130.000.

C

I think you made a slightly mistake. median 130.000 means 7 houses under or equal 130.000 and 7 houses above or equal 130.000

Since this is a must be true problem you have to try to find counterexamples

I) At least 1 house sold for > $165,000
we want to prove that all the houses have been sold by less than 165.000.
so let's maximize the value of the houses that are below the median (130.000) giving them a value of 130.000 now we have 8 houses with a value of 130.000 and the mean has to be 150.000, so the price of other 7 house have to account for this difference (20.000 *8 + 150.000 *7).
the medium price of the houses would be (20.000 *8 + 150.000 *7)/7 = 172857 bigger than 165.000 so it has to be true.

II) At least 1 house sold for > $130,000 but < $150,000
not necessary think of the configuration of the first statement
8 houses at 130.000
and 7 at 172857

III) At least 1 home sold for < $130,000
not necessary same as II
8 houses at 130.000
and 7 at 172857