DS Ques

[vivek.kapoor83]

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.

[jeegarm]

hi ,
The answer should be D for this

Best Regards,
Jeegar Mistry

[vivek.kapoor83]

can u just explain howcm D.

[Stuart@KaplanGMAT]

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.

Step 1 of the Kaplan method for DS: understand the question stem.

We know that for a set of 3 terms, the median is the middle term. Accordingly, the question is really asking "what's the price of the middle house?"

From the original question, we know that the sum of the three houses is $360k

(sum = avg*(# of terms) = 120*3 = 360)

Step 2 of the Kaplan method for DS: consider each statement, by itself, in conjunction with the information in the stem.

1) Tom's house is 110k.

So, the other two houses must add up to 250k.

Well, if the other two houses are 120 and 130, then 120 is the median. However, if the other two houses are 122 and 128, then 122 is the median. More than 1 answer: insufficient, eliminate (a) and (d).

2) Jane's house is 120k.

So, the other two houses must add up to 240k.

In this case, no matter how you slice up that 240k, 120k is still going to be the middle price. We can experiment if we want:

120/120/120... median of 120
119/120/121... median of 120
1/120/239... median of 120

For every possible set of prices, 120 will always be the median: sufficient, eliminate (c) and (e).

(2) is sufficient but (1) isn't: choose (B).

[Morgoth]

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.

T+J+S = 120000*3 = 360000
simplify this for easy working.


(1) The price of Tom’s house was $110
J+S = 360 - 110 = 250

if the distribution is 110, 120, 130, then 120 is the median.
if the distribution is 100, 110, 140, then 110 is the median.
Insufficient.

(2) The price of Jane’s house was $120
T+S = 360 - 120 = 240

if the distribution is 120, 120, 120, then 120 is the median.
if the distribution is 110, 120, 130, then 120 is the median.
if the distribution is 105, 120, 135, then 120 is the median.
Sufficient.

Thus, B is the answer.

[vivek.kapoor83]

Thanx Stuart.I also thought the way you did...but got confused in last step...Such a gr8 explanation. thanx

[Scott@TargetTestPrep]

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