Data Sufficiency

Hi ,

I came across this question in the official guide , P:323 :

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.

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Answer as per the book !:
Arithmetic Statistics
Let T, J, and S be the purchase prices for Tom's,
Jane's, and Sue's new houses. Given that the
average purchase price is 120,000, or
T + J + S = (3)(120,000), determine the
median purchase price.
(1) Given T = 110,000, the median could be
120,000 (if J = 120,000 and S = 130,000) or
125,000 (if J = 125,000 and S = 125,000);
NOT suffi cient.
(2) Given J = 120,000, the following two
cases include every possibility consistent
with T + J + S = (3)(120,000), or
T + S = (2)(120,000).
(i) T = S = 120,000
(ii) One of T or S is less than 120,000 and
the other is greater than 120,000.
In each case, the median is clearly 120,000;
SUFFICIENT.
Th e correct answer is B;
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Now I think there is another answer , which is Statement 1 is Suff , how is this :
Given T = 110,000, the median could be 110,000 if the prices of the houses are {100,000,110,000,150,000}
in this case the avg is 120,000 which is agree with the question and the median is 110,000 .
The question is not stating if 110,000 is the least value , so we can place it any where in the set !
following the same rule of statement 2 , the statment 1 is Suff .

What do you think ?

anasnet wrote:Hi ,

I came across this question in the official guide , P:323 :

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.

If the median can be only one value, the statement is sufficient.
If the median can be more than one value, the statement is insufficient.

Let T = Tom's house, J = Jane's house, S = Sue's house.
Sum = number of things * average = 3*120,000 = 360,000.
Thus, T+J+S = 360,000.

Statement 1: T = 110,000
Thus, J + S = 360,000 - 110,000 = 250,000.
The values could be J = 10,000, T = 110,000, S = 240,000.
Median = 110,000.
The values could be T = 110,000, J = 120,000, S = 130,000.
Median = 120,000.
Since the median can be more than one value, insufficient.

Statement 2: J = 120,000
Thus, T + S = 360,000 - 120,000 = 240,000.
The values could be T = 120,000, J = 120,000, S = 120,000.
Median = 120,000.
Only the values of T and S can be changed.
If the value of T increases above 120,000, then the value of S must decrease below 120,000, so that T+S = 240,000.
J will still be in the middle, so the median will remain 120,000.
If the value of S increases above 120,000, then the value of T must decrease below 120,000, so that T+S = 240,000.
J will still be in the middle, so the median will remain 120,000.
Since in every case median = 120,000, sufficient.

The correct answer is B.

GMATGuruNY ,

Thanks a lot...

I thought the same as Ana.. but now I understand .........