Babzsn84 wrote:

:oops: still not clear to me.

Can someone please explain??

Last month 15 homes were sold in Town X. The average (arithmetic 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 $130,0000 and less than $150,000

III. At least one of the homes was sold for less than $130,000.

A. I only

B. II only

C. III only

D. I and II

E. I and III

Note that we are asked which

MUST be true.

Given: \({x_1}+{x_2}+...+{x_7}+{x_8=130}+{x_9}+...+{x_{15}}=15*150=2250\)

Let's start with the first one and try to make it false.

I. At least one of the homes was sold for more than $165,000.Worst case scenario, when \(x_{15}\) has the least value (trying to make it less than 165), would be when \(x_1=x_2=x_3=x_4=x_5=x_6=x_7=x_8=130=max\), and \(x_9=x_{10}=x_{11}=x_{12}=x_{13}=x_{14}=x_{15}=min\):

\(8*130+7x=2250\) --> \(x_{min}\approx{173}\).

So we got that I is always true: At least one of the homes was sold for more than $165,000 (as for the worst case scenario we got that least value of \(x_{15}>165\)).

But if we take the scenario which we considered: \(x_1=x_2=x_3=x_4=x_5=x_6=x_7=x_8=130\), and \(x_9=x_{10}=x_{11}=x_{12}=x_{13}=x_{14}=x_{15}\approx{173}\) we can see that II and III with this scenario are false. So II and III are not always true.

Answer: A (I only).

In case of any question please post it here: last-month-15-homes-were-sold-in-town-x-the-average-128477.htmlHope it helps.

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