PS - Topic Mean Median ; Help needed GMAT around the corner

[soni_pallavi]

Hi

Could someone plz give an explanation for the below query?

Q3) Last month 15 homes were sold in Town X.The average 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. Atleast one of the homes was sols for more than $165,000

II. Atleast one of the homes was sold for more than $130,000 and less than $150,000

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

Thanks

[Brent@GMATPrepNow]

NOTE: The answer choices are very important here, since we can use them to find the correct answer through process of elimination. The full question reads:

Last month 15 homes were sold in Town X.The average 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. Atleast one of the homes was sold for more than $165,000
II. Atleast one of the homes was sold for more than $130,000 and less than $150,000
III. Atleast 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

Let's looks at one possible scenario and see which answer choices we can eliminate.

Aside: To make things simpler, let's divide all of the prices by 1000.

First, we'll use a nice rule that says: sum of all values = (mean)(number of values)
So, the sum of all 15 prices = ($150)(15) = $2250.

If the median is $130, then the middlemost value is $130

So, one possible scenario is:
130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 430

Aside: To find the last value (430), I took the sum of all 15 numbers (2250) and subtracted (14)(130)

Notice that this scenario tells us that II and III need not be true.

Since answer choices B, C, D and E all include either II or III, we can eliminate them.

This leaves us with A, which must be the correct answer.

Cheers,
Brent