M7MBA wrote: ↑

Thu Aug 27, 2020 12:39 am

Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?

(1) The price of Tom’s house was $110,000.
(2) The price of Jane’s house was $120,000.

Answer: B

Source: Official Guide

Given: The average (arithmetic mean) price of the three houses was $120,000.
This means (sum of the three house values)/3 = 120,000
Multiply both sides by 3 to get: sum of the three house values = 360,000

Target question: What was the median price of the three houses?

Statement 1: The price of Tom’s house was $110,000.
There are several scenarios that satisfy statement 1. Here are two:
Case a: The 3 house values are $110,000, $120,000 and $130,000. In this case, the answer to the target question is the median house price is $120,000
Case b: The 3 house values are $110,000, $110,000 and $140,000. In this case, the answer to the target question is the median house price is $110,000
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The price of Jane’s house was $120,000
Important: $120,000 is the average price of the 3 houses.
Since one house is valued at $120,000, there are two possible cases:
Case a: All three house prices are the same: $120,000, $120,000 and $120,000. In this case, the answer to the target question is the median house price is $120,000
Case b: All three house prices are the NOT same. In order for the sum of the 3 values to be 360,000, one value must be less than $120,000, and the other value must be greater than $120,000. So, the three house prices are: less than $120,000, $120,000, and greater than $120,000. In this case, the answer to the target question is the median house price is $120,000
In both possible cases, the answer to the target question is the same: the median house price is $120,000
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent