vivek.kapoor83 wrote: ↑

Thu Sep 25, 2008 10:57 pm

Q20:
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.

Solution:

Question Stem Analysis:

We are given that the average price of 3 houses is $120,000, which means that the sum of the 3 house prices is $360,000. We are to determine the median price of the 3 houses. Recall that the median of a set of 3 values is the middle value.

Statement One Alone:

If Tom paid $110,000 and Jane paid $90,000 and Sue paid $160,000, then the average would still be 360,000/3 = $120,000. In this case, the median price would be $110,000.

If Tom paid $110,000 and Jane paid $130,000 and Sue paid $120,000, the average would still be 360,000/3 = $120,000. In this case, however, the median price would be $120,000.

Statement one is not sufficient.

Statement Two Alone:

Jane paid $120,000 for her house. This means that the other two individuals could not both have paid more than $120,000 OR that they both paid less than $120,000 because, in either of these cases, the average house price could not equal $120,000. Therefore, we see that either of two situations could apply:

1. The first case is that all 3 paid $120,000. This would keep the average price at $120,000, and the median price would be $120,000.

2. The second case is that one paid less than $120,000, and the other paid more than $120,000. We know that Jane paid $120,000. Thus, no matter what the other two paid for their houses, Jane’s purchase of $120,000 would be the median price.

Statement two is sufficient.

Answer: B