# GMAT OFFICIAL GUIDE DS – Tom, Jane, and Sue each purchased…

## Solution:

We are given that Tom, Jane, and Sue each purchased a new house. We are also given that

the average (arithmetic mean) price of the three houses was \$120,000. If we let T = the

price of Tom’s house, J = the price of Jane’s house and S = the price of Sue’s house, we can

create the following equation:

(T + J + S)/3 = 120,000

T + J + S = 360,000

We need to determine the median price of the three houses. Thus, we need to determine,

when the prices of the houses are ordered from least to greatest, the middle price.

Statement One Alone:

The price of Tom&#39;s house was \$110,000.

Because T = 110,000, we can determine the sum of J and S.

110,000 + J + S = 360,000

J + S = 250,000

Thus, the sum of the prices of Jane’s house and Sue’s house must be 250,000. We can split

this sum up in a number of ways, and doing this will give us different values for the median

home price. Let’s test two different cases:

Case #1

T = 110,000

J = 100,000

S = 150,000

Median = 110,000

Case #2

T = 110,000

J = 120,000

S = 130,000

Median = 120,000

Statement one is not sufficient to answer the question. We can eliminate answer choices A

and D.

Statement Two Alone:

The price of Jane&#39;s house was \$120,000.

Because J = 120,000, we can determine the sum of T and S.

120,000 + T + S = 360,000

T + S = 240,000

Thus, the sum of the prices of Jane’s house and Sue’s house must be 240,000. We can split

this sum up in a number of ways; however, regardless of how we split up 240,000 we will

always get the same median home price. Let’s test a few different cases:

Case #1

J = 120,000

T = 120,000

S = 120,000

Median = 120,000

Case #2

J = 120,000

T = 110,000

S = 130,000

Median = 120,000

We see that the median will always be 120,000. Statement two is sufficient to answer the

question.