Inductive Quant

damilolaamele wrote:Please can someone assist me with this question? Been trying to figure out how to approach it.

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 $165,00
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

a) I only
b) II only
c) III only
d) I and II
e) I and III

[spoiler]OA: A[/spoiler]
Source: GMAT Practice Test.

Let's looks at one possible scenario and then 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

I'm not entirely sure what you mean.
Are you asking what I'd do if one or more of the three statements were different, or what I'd do if one or more of the five answer choices were different?

When it comes to questions asking what must be true, it's often easiest to eliminate answer choices by looking for counter-examples. Alternatively, we must use some math/deductive to demonstrate that a certain statement is always true.

I hope that helps.

Cheers,
Brent