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Last month 15 homes were sold in town x. The average(airthmetic mean)sale price of the homes was $150,000 and the median sale price was $130,000.which of the following statements must be true? I. At least one of the homes was sold for more than $165,000 II. At least one of the homes was sold for more than $130,000 and less than $150,000 III. At least one of the homes was sold for less than $130,000

1. I only 2. II only 3. III only 4. I and II 5. I and III

The mean and Median are close from that we can induce that the sale price spread is evenly balanced. I. can be true but we really cant decide with the given data. II.This as well cant be sure. III.as the median is $130,000 so there must be sale price less than and more than it.

Last month 15 homes were sold in town x. The average(airthmetic mean)sale price of the homes was $150,000 and the median sale price was $130,000.which of the following statements must be true? I. At least one of the homes was sold for more than $165,000 II. At least one of the homes was sold for more than $130,000 and less than $150,000 III. At least one of the homes was sold for less than $130,000

1. I only 2. II only 3. III only 4. I and II 5. I and III

It is indeed A.

Here's why:

Take statement 2: It says that at least one of the houses must have been sold for a value between 130,000 and 150,000. Not necessarily. See this case.. The median is the 8th number and its value is 130,000. If the 7 numbers before the median have a value of 130,000 too, total revenue from these 8 house sales is = 1,040,000. Now total revenue from all the 15 houses is 2,250,000. Now the rest of the 7 houses must each be sold for at least c.172,000 (approx) to cover teh balance (2,250,000 - 1,040,000). Agreed, that one of the houses could have been sold between the bracket given (130,000 and 150,000) but this is not a must be true condition. It could well be that all are sold at the same price (approx 172,000)

Statement 3: Again, not a must be true statement. All the houses before the mdedian could have been sold for 130,000. The ones above the median must be sold for above the median (at least some of them).

Now statement 1: This has to be true. The MAXIMUM contribution that the first 8 households can make towards total sales is (8 * 130,000 as calculated above). Now to fulfill the balance, even if all the houses after the median were sold at the same price, they would sell for approx 172,000 each, which is greater than 165,000. If any household was sold for less than 172,000, there would have to be another household selling for more than 172,000 to cover the balance.