IMO C

Please provide explanation

The answer should contain third option as a must, because it is median price, so at least 1 house should cost less. ABD are out.
Fro the information given we cant find if there was sny house >165000$, so C is the best answer.

sanjana wrote:Last Month 15 homes were sold in town x.The Avg Sale price of the houses was $150,000 and the median sale price was $130,000. Which of the following must be true?

I - Atleast 1 house sold for >$165,000
II - Atleast 1 house sold for >$130,000 but <$150,000
III - Atleast 1 house sold for <130,000

a)I
B)II
C)III
D)1 & II
E)I & III

a?

analyzing each statement as follows:

I: if median = 130K 14 houses could have sold for 130K making the 15th house sale worth >165 in order to get an avg of 150K --> a

II: all we know is that at least one house sold for 130K, we still don't know if a house was sold for >130 and <150

III: all we know is that at least one house sold for 130K; we could have a situation where all houses but 1 is 130K; the odd one must be more than 130K to give an avg of 150K hence III needn't be true.

pls let me know if I have missed anything.

OA is A.

Thanks for your help!

Another way of knocking all three statements at one shot:

Total cost for all houses - 15 * 150 = 2250
Lets say 8 houses are at median price - 130 -> total cost of 8 houses - 8 * 130 - 1040

Balance 2250 - 1040 = 1210; Cost per house of rest of 7 houses - 172 (rounded off).

1. Must be true as per above calculations
2. Need not be true
3. Need not be true as per above calcluation

HTH