Mjkourtis wrote:Last month 15 homes were sold in Town X. The average sale price was $150,000 and median price was $130,000. Which of the following must be true?
I. At least 1 home was sold for more than $150,000.
II. At least 1 home was sold between $130,000 and $150,000.
III. At least 1 home was sold for less than $130,000.
A. I
B. II
C. III
D. I, II
E. I, III
The key word in this question is
MUST. So, if it's possible that a scenario is not true, we can eliminate it.
So, 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 our scenario does not conform to either one).
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
