Statistics Doubt

ani781 wrote:(A) Last mnth 15 homes were sold in town A;
The avg sale price of the homes was 150,000$ & the median was 130,000$.
Which of the following statement is true?
1. Atleast one of the homes was sold for more than 165,000
2. Atleast one was sold for more than 130,000 and less than 150,000
3. Atleast one was sold for less than 130,000

a) 1 only
b) 2 only
c) 3 only
d) 1 & 2
e) 1 & 3

I am not sure the logic...

Let's look 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 then I subtracted (14)(130)

IMPORTANT: Notice that this scenario we just created does not conform to statement 2 (At least one was sold for more than 130,000 and less than 150,000 ) and it does not conform to statement 3 (At least one was sold for less than 130,000)

In other words, statements 2 and 3 need not be true.

Since answer choices B, C, D and E all include either statement 2 or statement 3, we can eliminate them.

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

Cheers,
Brent